Trevisa's translation of the mathematical section of Bartholomew's De proprietatibus rerum

Item Type text; Thesis-Reproduction (electronic)

Authors Dederich, Robert Marwood, 1916-

Publisher The University of Arizona.

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Link to Item http://hdl.handle.net/10150/553553 TREVISA'S TRANSLATION

OP THE MATHEMATICAL SECTION OP BARTHOLOMEW'S

"DE PROPRIETATIBUS RKRUM”

Edited, with a glossary and notes,

from the British Museum MS. Additional 27944

by

Robert M. Dederich

A Thesis

submitted to the faculty of the

Department of English

In partial fulfillment of

the requirements for the degree of

Master of Arts

in the Graduate College

University of Arizona

1941

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PAOB IRTTtODUCTICH...... } ...... Ill

The purpose of this thesis ...... • ill

The problem ...... 111

The manuscript ...... v

The author •••••••*••••••••••*• lx

The translator...... xl

The contents of the t e x t ...... xll

An estimate of the Importance of the manuscript v . xvll

TEXT...... 1

APPENDIX...... 46

Votes on the text • • ...... 46

Reproduction of manuscript page ...... 54

Transcript of last chapter of manuscript...... 66

Transcript of list of sources given in manuscript • 56

Bibliography ..•• ...... 58

GLOSSARY...... 60 The purpose of this thesis is twofold: first, to aid in seme degree the history of science by making available an edition of the mathematical portion of a popular medieval textbook; second, to contribute to the work on the work on the Middle English Dictionary which is being prepared under the editorship of Professor Thomas A* Knott mt the University of Michigan.

Science has been under fire since it first began. In early times the scientist was charged with magi#; in modern times the scientist is charged with the construction of modern Instruments of warfare and the promotion of unemployment. Early scientists justified to our ancestors the fact that they felt like having three wives at the same time by the concurrence of Wars and Venus at their birth; when, however, the knowledge of the same stars served to guide the enemy to his seacoast prey, astronomy was eyed askance. Modern scientists provide us with magnificently speedy transportation on our errands of mercy or Babbitry; when, however, the airplane seems likely to drive the population of the earth underground, it is felt to be a not unmixed blessing. Science proposes and man dis­ poses; and man, having disposed, questions the wisdom of science.

Political commentators have suggested that the fault may lie with - l ' - our society, not science. Bernal has the following statement on the subject:

The economic Instability of the present system can hardly be charged directly on to science even by its worst enemies. Tim truth that -iv-

theip charges contain, however, is that the present economic system and the advance of science cannot for such longer go on together. Either science will tie stifled and the system Itself go down In war and barbarism, or the system will have to be changed to let science get on with Its Job.

In our modern world of viciously weighed propaganda and magnificent facilities for communication a point of view which tea reason for Its basis Instead of emotion la under a handicap. The lamp of reason burns with a small, clear light, not with the great red flare of opinion. And the advocates of a scientific eolation of the world*s difficulties are pricked with the small but persistent fear that there m y not be victory

In the future. Bernal2 states the case quite clearly when he says:

We have seen. In the ccurse of history. Institutions grow up, stag­ nate, end die away. How do we know that the same will not happen to science? Indeed, the greatest burst of scientific activity before the present age, the science of Hollenletle times, which had also become an Institution, faded away long before the society In which It had been born was Itself destroyed. How do we know that the same will not happen and, indeed. Is not happening to modern science? It is not sufficient In answering theme questions to make an analysis of the present situation of science. A full answer requires a knowledge of the whole history of science. Unfortunately, the history of science as an Institution in relation to social and economic events has not yet been written or even attempted. Exis­ ting histories of science are little more than pious records of great men and their works, suitable perhaps for the Inspiration of young workers, but not for understanding the rise and growth of science as an Institution. Borne attempt at such a history met, however, be made If we are to understand the significance of the institution of science as It now Is and Its complex relationships with other Institutions and with the general activity of society. The key to the future of science lies In its past, and It Is only after examining it ... that we can begin to determine what la and what may become the social function of science.

This thesis may, in some small degree, aid la the future study of the history of science by making available a workable text of the aeeount of mathematics contained In a widely known textbook of the fourteenth and

8. Bernal, pp. 11, 12. The work done for the Middle English Dictionary has been the choosing of words from this manuscript, the deciding upon meanings of these words, and the transmission of the words with transcripts of the context to the editors# Between three hundred and fifty and four hundred

This is an edition of the British Museum manuscript Additional

No. 27944, John Trevisa's translation of Bartholosaeus Angllcus pe Pro- prletatlbus Rerum, Book XIX, chapters CXVI to GXXX inclusive (manuscript leaves 326a to 333a). This manuscript is the basis of the following text; it is referred to throughout by the abbreviation nT8f Two other manu­ scripts have been used in editing. The printed Latin edition, Paris,

Blbl. St* Genevieve, manuscript No. 1024 (frames 247 to 272, referred to as "LB”) is a Latin copy of the manuscript from which Trevlsa made his translation, and the printed edition of Rynkyn de Worde (pages 918 to 940, referred to as nS?dWu) Is simply another — later — Middle English text.

These two manuscripts were consulted simply to throw light on TB, and the text which ia given below is not an attempt to give all variants among the three. All significant variations are noted; minor variations are omitted.

The dates of the three manuscripts are: TB, c. 14Q0p3 LB, 1483;* fids, 1496.

TB is not the original from which KdS was copied. This is shown by the presence in RdS of information which does not appear in TB; examples

3. See Appendix, at the beginning of the list of authorities quoted, for Trevlsa1 s date of 1398; tMe manuscript is not the original, but it is an early copy. 4. At the end of IS is the following note: "Impreasus et completus per me Johannem Koelhoff de Aubeek Colonle elute(m) Anno gr(atla)e .Mcceelxxxllj. In vigllla Sebastian! martyris.* of this are In the following notes: p. 2, 2; p. 3* 4; p. 10, 3? others say be cited. Considering the great number of copies of this work which have survived (the Blbllotheque National# at Faria alone holds eighteen6) this Is not surprising.

In passing It my be noted that LB shows evidence of mioh more exact phrasing than either TB or Wdf? (which follows TB closely). fthlle the Latin

Is certainly decaying, as shown by a comparison of. Isidore and LB, yet It

Is still clearer than the English of the time. Thorndike,8 speaking of this same manuscript, tolls of the Impression that "Men apparently could think more directly In Latin In the thirteenth century than they could express themselves In English In the fourteenth or fifteenth century."

The manuscript T3 Is printed In a small, clear hand and Is quite legible, a sample page is reproduced In the Appendix, and from this It will.bo noted that the Latin characters are used. Two of the Old English characters carry over, namely the thorn (line 1, bat) and the old type s.

(line 1, paaaob). The Roman numerals at the side of the manuscript are iadleatlono of book and chapter numbers and are not In the original. The number at the upper rlghthand corner Is the leaf number (827a) and is also a modern addition.

The abbreviations used are those prevalent In the Latin manuscripts of the time. A line over a letter, as in soame (line 4), means a following nasal; In line 12 In the word frerlnne the abbreviation for an £ preceded by a vowel occurs; the abbreviation for ua appears la line 16 in the word quGntltQQa; the word departed In line 19 contains the abbreviation for a

S. L. Thorndike, History of Magic and Experimental science. 1923, II, p. 405. 6. Ibid.. XI, p. 410. -vll-

following £ plus a vowol. Two other abbreviations (not found on the page reproduced In the Appendix) occur Infrequently: at the end of a word, us la represented by a small superscript nine, and -rum is denoted by con­ tinuing the horizontal stroke of the form of r which looks like a 2, (as in noabre. line 1) and crossing it with a diagonal.

In the manuscript there is little or no punctuation; consequently the punctuation which appears in this edition has been inserted. The punctuation is placed in the text simply break*She thought eontent into smaller pieces; commas, semicolons, colons, and periods are used simply to provide breaks in continuity, of ascending strength in the order given.

The double £ (ff) to indicate a capital letter has been retained in all cases. In most cases tills Indicates a capital at the beginning of a sentence. When it has seemed beat to begin the sentence in this edition at another point the double £ has been retained, oven if there is no other justification for it.

Round brackets around a word or letter in the text mean one of two things: either an emendation has been made in the text, or additional reference setter is given. The great number of the additional references inserted in the body of the text are to the Orlglnes of Isidore; these consist of three numbers separated by periods, and the numbers represent book, chapter, and topic In the Oxford edition. Concerning the eeeddations: an insertion not covered by a footnote was made to aid the sense, and it may be disregarded if It la not needed; an insertion with a footnote will be found justified at the bottom of the page.

It seems worthwhile, in closing this discussion of the manuscripts, to Illustrate the ways in which errors come about. The following passage via

Is transcribed from the four texts I have had access to. Isidore

Cnolata vaaa argentea vel aurea sunt, slgnls emlnontlorlbus Intus extrave expressa, a caelo vocata, quod est genus ferramentl, quern

LB

Gelata aunt vaaa aurea vel argentea slgnls euldentlorlbus Intus vel extra’ expressa a celo dicta quod est genus farrsaontl quod vulgo . clllonea vocat ut (licit Isl. m

algne »l$>lnne or wl$>oute and habbe& >at nams of telum $>at Is an Instruaeht of ^ree $»at comynllohe eleped oylloon as Ysld scl&.

Hdrr

Tolata ben vessels of god or of syluer markyd wyth euydent sygne sythln other vlthoute. And hathe $>at name cf Yolua that Is an Instrument of thre Bat Is oomynly callyd Clllcon as Isyder aayth.

Since Trevlea was a Cornlshmn by birth and spent much of his life

show southern dialect characterIstlss. It doest but the Indications

Trevlsa's Southern, as shown In the manuscript Cotton Tiberius D VII, his translation of Hlgden*s Polychronlcon (a contemporary manuscript In pure southern, according to Emerson7), shows "no voicing of Initial f, j), 7 and s, so far as orthography Is concerned.n It does show, however, "a, for ha (beside hi, hy_In the plural of the third personal pronoun,"7 furst for Midland first, choose for Midland obese (choose).8 The text of the trarolatlon of Bartholomew1 s book shows fewer Southern charaeWlstlcs;

? 0. P. Emarson. A Kiddle English Eonder. 1938. p. 311. 8. Ibjd*. pp. 220-826, where Book I, chapter 69 of the Polychronlcon is given In Trevlaa’s translation. •I*-

m occurs for Midland I, £ (In furatt. yunds. y-huddaK but this retention of the Old English sound of % Is not consistent throughout; - # as the plural ending of the verb (tweye lynes bat touchofr olper oper; tweyne, oon, and frre make# euene slxe; we knowep) Is also a mark of Southern Influence.9

There has been, however, aonophthonglng of eo and ea (In aeuono. heuene) as there was not In tiie text of the Polvehronlcon discussed above.

la morphology the manuscript shows some conservatism. Indicating

Southern origin; he occurs with in two succeeding lines, showing the earlier and later forms of the third personal pronoun together; the past . • : participle has the prefix £- In most cases, although there are exceptions.

In general, however, the inflectional endings have disappeared, showing only slngalar, plural, and genitive as in Modern English, and the verb form have simplified.

Little is gained by theorizing upon the language of a popular text such as this. Scribes not only change the spelling and wording to suit themselves but also make errors, and there is no way of knowing which is which. The only consistency Is In Inconsistency, for the errors are cumulative. Let it suffice to say that the manuscript shows traces of

Southern with a majority of Midland forms.

The account of Bartholomew given below10 was felt to be the one best suited to the purpose. It Is reproduced verbatim with tills exception, that the bibliography which follows this section In Barton la omitted.

8. Emerson, p. clll. 10. o. Barton, Introduction & Shs. History j£ Science. 1931, II, Pt. 2, pp. 686, 687. BartholoaaeuB Angllcus, Maglster da proprletatlbee perm. The name Bartholomew da (Jlanvllle, which la uncertain and probably wrong, should bo avoided; It was first used perhaps because of a confusion with another English Franciscan bearing that name, who died In 1360.

Bartholomew was born In England; ha flourished in Oxford, Paris (c. 1280), Magdeburg (after 1230); he was a Franciscan of the French province; ho mat have lived until about the middle of the century, for he quotes Michael Scot and Grosseteste; he Is quoted by Bacon. He was perhaps a pupil of Grosseteste. He wrote, c. 1830-1240, for the plain people (slmpllces et rudes) an encyclopaedia entitled De proprletatlbua rerum, which ms Immensely popular for about three centuries, though it m s already behind the times in many respects when It was composed. Its popularity is witnessed by the number of manuscripts, translations, and editions. It was one of the books which the Paris students could hire for a definite price. The aim was primarily theological and philosophical, but Bartholomew had a genuine taste for natural history. His work Is divided Into nine­ teen books of which the contents can be roughly indicated as follows: (1) God; (2) angels and demons; (3) psychology; (4-5) physiology; (6) family life, domestic economy; (7) medicine (largely derived from Constantine the African); (8) cosmology, astrology; (9) time divisions; (10) fora and matter, elements; (11) air, meteorology; (12) flying creatures; (13) waters and fishes, dolphins, whales; (14) physical geography; (15) political geography, (In 175 chapters; this contains a number of Interesting remarks, notes on economic geography, etc.); (10) gems, minerals, metals; (17) trees and herbs; (18) animal*; (19) color, odor, savor; food and drink; eggs; weights and measures; musical instruments.

It Is clear that Bartholomew1^ encyclopaedia was remarkably com­ prehensive and methodical. But on the whole it represented a state of knowledge which was already superseded. For example, his astronomy represented the early mediaeval tradition, that of Maerobius (first half of fifth century) and of Martlanus Capella (second half of fifth century), and hence It Included allusions to the geo-hello- eentrleel system of Heraclldce of Pontos. His geography and natural history were more advanced, and his descriptions of plants and animals contain original touches which are exceedingly delightful. His herbal was by far the most notable owrk of its kind written by an Englishman In the Middle Ages. The political geography of Europe contains a quantity of Information which had not been put together before.

Hla account of the divisions of time Is curious: the day Is divided Into twenty-four hours, the hour Into four points or forty momenta, the moment Into twelve ounces, the ounce into forty-seven atoms (thus there are 22660 atoms In one hour, as compared with our 3600 seconds). An earlier encyclopaedia, the IaBP-,0 mundl [Footnote in Sarto*: Probably compiled by tionorlus Inclusus (second half of eleventh cen­ tury. See vol. 1, 749)j , which shared the popularity of Bartholo­ mew’s work, explained the same division of the hour (but Its hour was double, one twelfth part of the day), but also others Into tern minutes, fifteen parts, sixty osteats.

The £e proprletatlbua rerun was translated into Italian by Vlvaldo Balealzer of Bantova In 1309; Into French, by Jean Gorbechon for Charles V,In 1372; into Provencal before 1391; Into English by $ohn of Trevlsa In 1397 or 1398; Into Spanish by Vincents (Vineaat). of Burgos some time in the fifteenth century. This last named trans­ lation is a classic of the Spanish langiage; it is registered in; the Catologo de autorldades de la lengua.

Little, cc^paratlvely speaking, is known of John Trevlsa (1326-1412), one of the important figures of our early prose literature. He was born in Cornwall, educated at Exeter and Queen’s Colleges in Oxford. In 1379

(according to the Dictionary of National Biography; the Cambridge History of English Literature. II, p. 38, gives the date of 1376) he and three others were ejected from Queen’s College; they were not apparently in any disgrace to speak of, for Trevlsa rented rooms there in 1395 and 13##.

He became vicar at Berkeley in Gloucestershire and spent most of his later life there. Ehlle not an original writer he wag a diligent translator; his two most ambitious works are translations of Higden’s Polyohronloon and Bartholomew’s Do Proprlotatlbus Rerun. Both of these were done at the request of Thomas, Lord Berkeley, whose chaplain Trevlsa was. The

Polyohronleon is more important in the history of literature. It is evident from his translation of £e Proprletatlbua Rerua that he was not too exact a scholar, for at times he is simply translating the words that appear and is not rendering the sense; an example of this is his explanation of first and Si 11 11

11. See p. 13 of the text, footnotes 3, 4. -XS1

»• ties material la handled In a

Medieval na tie* different conceptions of numbers run through It. First, there Is what *a now call Hnumber theory,n or the consideration of numbers with no regard to processes In which they may be used but only In their Interrelations among themselves. Secondly, there is the knowledge current at the time of arithmetical, geometrical, and algebraic processes. Thirdly, there is the ever-present number symbolism, the mystical or philosophical attributes of numbers, with which men have concerned themselves from very earliest history to the present. The discussion of the contents of the text will be covered from those three points of view.

The number theory treated here Is mostly hearsay retailing of the doctrines of the Pythagoreans. From the errors made It seems probable that the writer was not familiar with his subject to any great extent and that he had not progressed far enough in the study of It to have the Ideas clearly In mind when he wrote. The exposition of perfect numbers, for

There Is no question of synthesis here. The knowledge is set down and left for the reader to use as he can and as It suits him. what In­ formation has been given Is Inadequately explained for the previously uninformed reader, and the principles given do not constitute a thorough -Kill

discussion of the subject In any case.

Ten appears to have been recognized as the basis of the number system,

for Mthe number of ten is first source of numbers and no number is greater

than ten that is not composed of ten plus another number,” and so forth.

Even and odd numbers are discussed, and these two classes are divided Into

smaller classes of combinations of the two. Superfluous, diminutive, and

perfect numbers are taken up and accorded fairly clear treatment, following

which simple, compound, and mean numbers are discussed. Numbers may be

compared with each other, it is noted (p. 14), and the names of the different

comparisons are given. Follows a short discourse on discrete and contained

numbers (p. 16), an explanation of the geometrical representation of numbers (p. 16), another and slightly different approach to the problem of even

and odd numbers (p. IS), and the discussion of number theory is complete.

k short discussion of geometry Is given next (p. 20) la which these matters

are taken up: various plane and solid figures with the names and (in­

accurate) diagrams of them (p. 21); the finding of the mean proportional

is geometry (p.22); the circle (p. 28); the triangle (p. 24); the angle (p. ft). Immediately after this (p. 88) the discussion of weights and

measures begins, and the remainder of the manuscript la devoted to it.

The theory of numbers and the background material of geometry are

covered slightly, perhaps adequately for encyclopedic purposes, but com­

putation and the essential processes are given scant attention. The con­

trast shown In the discussion of such matters as unity and the point, with

such concepts as the geometrical figures and the one mathematical process

mentioned, proportion, show the writer to have been Interested in mathe­

matics from the point of view of the theologian and philosopher only, and

to have had little understanding of the use of numbers. There were ■xtw

treatises on mathematics as such available at the time; Bede and Alculn, to mention only two, who ere both listed at the end of the manuscript as sources for parts of the encyclopedia, wrote on methods of computation; this part of their works, however, has bean disregarded. Bartholomew simply follows the lead of Isidore,who "gives definitions and grammatical explanations of technical terms, but does not describe the mcxlea of com­ putation then in vogue."18

Philosophically speaking, dealing with number symbolism, Bartholomew

Is on more familiar ground; more than five pages are given to the con­ templation of unity, or one, 1» its various ramifications. Much of this discussion comes from Aristotle’s Metaphysics. The eight other digits are then taken up In order and their properties listed, and much of this discussion Is pure symbolism. Two Is considered by some an Infamous number because It Is the first step removed from unity or perfection; another author, however, has it to say In praise of two that it Is but little removed from perfection, that It Is nearest of numbers to one, and thus Is not such a bad number after all. Three Is the token of the Trinity; four represents the square, a stable figure, and is taken to mean the stableness of the church; five Is the symbol of the knowledge of the faith of the Trlmlty; six Is the sign of perfection; seven represents the seven graces; eight is the heavenly bliss that shall be his who has the seven graces on earth; nine Is the angel#number; ten Is the limit of simple numbers and represents Christ, who la the beginning and ending of all simple creatures, animals and men.

Throughout the discussion of numbers this symbolism keeps recurring.

18. P. Cajjorl, A History of Mathematics. 1919, p. 113. with symbolism. Modlus (p. 89) Is a

it s» ted

tl Testament, an, great Blgilfi- In this

bow 1 rooted in medieval thought was the conaolousness of numbers, not as mathematical tools, nor yet as the counters in a game, but as fundamental realities, alive with memories and eloquent with meaning. The fact that 3 disciples were present at the transfigura­ tion was, in the Middle Ages, a circumstance not to be lightly passed over.

It has been said above that the Pythagorean doctrines are reflected in this work. Aristotle*a survey of their beliefs ("the most complete extant survey of early Pythagoreanlam” according to Hopper ) is given below.

The first' to take up mathematics ... (they) thought its principles were the principles of all things. Sine# of these principles numbers are by nature the first, and in number they seemed to see many re­ semblances to the things that exist and come into being — more than in fire and earth and water (such and such a modification of numbers being soul and reason, another being opportunity — and similarly almost all things being numerically expressible); since, again, they saw that the modifications and ratios of the musical scales were expressible in numbers; — since, then, all other things seemed in their whole nature to be modelled on numbers, and numbers seemed to be the first things in the whole of nature they supposed the elements of number to be the elements of all things, and;the whole heaven to be a musical scale and a number. And all the properties of numbers and scales which they could show to agree with the attributes and parts and the whole arrangement of the heavens, they collected sad fitted Into their scheme; and if there was a gap anywhere, they readily made additions so as to make their whole theory coherent. 1314

13. V. P. hopper, Medieval Humber Symbolism, 1936, p. vlil. 14. Hopper, 33, 34. PythagoreanlBm cams to the Middle Ages largely through the writings of Hlcoaachus, whose Influersie upon this text Is evident. Comparing his definitions of even and odd numbers, for Instance, with the ones given In the text, we find almost exact parallels between Trevisa's English and the English translation by Heath;16 Hleomchus has: "That is even which Is capable of being divided Into two equal parts without an unit falling In the middle, and that Is odd which cannot be divided Into two equal parts because of the aforesaid Intervention of the unit;* Trevlsa has: * N euene nombre may be deled euene atwynne and leue nougt oon oon, but fee odde nombre may nou3t be y-deled euene atwynne wl&outen ocm odde.w 16

The Pythagoreans1 definition Is also given by illcomacbuo16 "An even number Is that which admits of being divided, by one and the same operation, Into the greatest and the least (parts), greatest In size but least In quantity. Our text has: R0j>er by Plctagoras lore his nombre may be y-deled vnder J>e same dyulsloun la lasts and In most: In lest diuioloun and most grete noabre.n 16

Klcomchus notes two other definitions of even and odd numbers, both of which are paralleled by passages in Bartholomew’s work. An even number,

1#' according to Hlcoaachus, may be divided Into two parts, and the parts may be even or odd; but If one is odd, the other Is odd, and If one Is even, the other must be even. Odd numbers can be divided only into unlike parte, one odd and one even. Lastly, an even number la made by adding one to an odd, and an odd number by adding one to an even. For the correc­

ts the text see pages 18 and 19.

1C. T. L. 1926, II p. 281. 16. Text, pp. 18, 19. -xvli

blnationo of ovonnaas and oddneaa found In numbers, and prime and com­ pound numbers. He17 considers prime numbers and compound numbers as divisions of the class of odd numbers, and Bartholomew begins hla dus- cusalon of these numbers with the words, "Vneuone nombras ben dlulded In IB *ls wise. Somme ben simple end soame compound and soaao ben mens."

Bartholomew’s arithmetic ernes from Klcoiaachua of Qeraaa through

Isidore, who copied from Boethius, who copied. In his Do Institutions

Arlthaotlca. directly from Hlccxmchus.'19 This line of writers were not

Interested as much In arithmetic as a science as they were In the philo­ sophical Implications which they could find In It.

' • M jgililM JSl tfae importance o£ £&£. panuscrljBt. D. B. ^Ith gives the oplnltm20 that the mathematics of this work can be dismissed as being simply an abridgment of Boethius (through

Isidore) and having little or no value to the historian of science. This statement Is true only In a very limited sense: It Is not true for any­ one who intends to Investigate the mind of the scientist through the years.

These men thought they were scientists. In these Middle Ages men "cannot yet consistently discriminate between occult science and natural science, between magic and applied science."81 They cannot yet tell the difference between metaphysical dreaming and experimentally-proven truth. They are addicted to the "pernicious and inveterate habit of dwelling upon abstractions

Study has revealed "In the medieval mind a weblike structure of abstract

17. Heath, II, p. 28?. 16. Text, p. 18. 19. Cajorl, m t , p. 6f. to. D. B. Smith, History o£ Mathematics. 1923, p. 184. 81. Thorndike, II, p. 983. 28. Bacon, quoted by Bernal, p. 6. -**111

Ideas and concrete realities so closely Interwoven and Interdependent that no serious gap was felt to exist between them. In consequence, what appears to the modern mind as a conscious and often artificial and strained divipt- tlon from simplicity and sincerity was more often than not an entirely

81 • natural mode of expression."

The Importance of this manuscript and others like it is this: Progress comes from a reversion to first principles and the firm basis of Investi­ gation upon those first principles. This manuscript shows men basing their thought upon erroneous principles, principles dreamed Into existence and watered by en unscientific dependence upon authority. It should be learned from manuscripts liko this that hypotheses have no validity until they are proven; that theories are merely words until they are tested; that opinions do not gain In truth simply because they are forcefully asserted.

23. Hopper, p. *11 BOOK XIX

Capitulua CXVI, Do zmororua (Difforcnciis)1 nensurarm ponderum ot sonorua.

To Jjo Toraaido proprotoea of $>inges it aenep ao good atto laste to motto oomwhat few© and lights of J>e proprotees and diaersitees of nonbroa, of nesures, of wi^tee^ and of eo(vm)oo.^ For as laid. Bci|), li.° 5° (3.4.1)

resoun of nombroo is nougt vrorfey to bo despised} for in many place of holy writ it schowop how nocho mistorio and priuoto is in resoun of nonbres.

For it is not y-soid an ydil in hasto, I nade alio in nonbre, wighte, and mesuro, as it is y-ooido Sapen(tia) li.° xi° (11.21). For pe nombre of

sixes pat is perfite and y-mado of his owne parties toknep pa perfltaeaee

of po world*. Mad so it is to vnderstoade of opre nonbres. Aid no ping we nay knows and cormo xvipout lore of noabros} for par by wo knowop hour os

and tymes whanno we dispatch of pe cours of po monpes; while wo l:nowep

(pa.t) pe spaa* of gores, pat coraep about* by noumbre, bap y-taught pat

we ben nougt y-schent in acountes. fatal away, ho seip, noumbre and tale

and all© pinges hep y-loet. Do away compot and acountoa and al is ful

of lowednesso and vneonnynge, and no diuersite is bitv/ene opre besteo

and men pat knowep nougt pe resoun and calculynge and of acountis, as

loid. seip pore (5.4.2-5). Also in pe bigynnyngo of ars metric it is

y-ooid pat it is neuere y-knowe what is a triangle vdpoute po nombre of

1% TB not clear (d— onciis)} WdTJ differenoiis; LB no corrosponding word. 2. TB GomoB} Wdg sommos} LB sonorum. . -2~

J>ro, nou^er a quadrangle wijjoute t>c noumbre of fcure, and bo of o&re.

And so it is y-knowo J>at no $>ing is y-knowe by science nathcmtica wijjoute noabre, as bo eeib Jiere (3*4.4). Also, as he sei)> $>ere (3.5.1), a nombro is a multitude y-gadred by of to takyng of oon; for oon is |>e roots and ooder of nombrcs. And oon is nougi many. Oon coaeji nongt of o^er nombre, but oon is $)3 blgyragnag and wello of alle noabres, and Jxsrof alio noobres come)? and springe)). For oon is ))e rooto of )>e manye of multitude and of nrultiplicaeioun and is most simple and worjd and most virtuous of alle )mt be)) conteyned )>ervndor, as Ar(istotlo) seib and Auicenne 1U° (i) c.° 20.1

Ffor oon is more and root® and wolle of multitude; oon conteyneb alle vnder itself, and alio bingos beb berlnne as in the fengir as he seib c.° 54°.

For be proprote of oon is to make multitude, and to give berto boynge, and to bo in alle parties barof, and conteyneb simpliciter as it is y-seide li.° iiij0 c.° ij°. And for oon is be T?elle of alle bingos, be none a bing nyeb (to vnite, be more he nygheb) to sobnes and troube as he seib c.° 2°. Ffor oon is as it wore be forme and. tweyno as it were bo matierej and berforo b= °oro a bing neigheb to oon po more he pasaib fro doubilnes and neigheb to simplonesse, and be more ho neighob to boynge. Ffor beynge is noust tofore oon as it is y-seide libro 9°jt and oon is nou5t dyuers but by be matiere, for he susteyneb and wibholdib alle binges as it is y-seido li.° 5° c.° 31°. Oon and vnite is so y-preised among rriso men bat many men neneb bat oon and vnite is b° soule in noabros, ber coaeb of oon and of vnite; and meneb bat oon is bigyrmyng of all binges bat

1. TB I li.U c.v 2W; LB li. i.C.ij. ' S* TB bn more a bing nyghob to sobnes and troube; LB quanto plus res appropinquit vnitati. tanto plus appropinquat veritati; W S the more a thyngo nygheth to ono and vnyte tho more it nyghoth to eothnosse and is continual and discrete as Auiconno sei$> li.° 3° c.° 1°. Also oon is

y-proised for he coec£ of none oi)or, and alle o^or noabre comef l>orof,

and is y-brongt i>erfco as to $>s proper heed and vralle per of as ha oeip.

Also for synpilnes oon is nou5t y-delsd ne y-parted as he seip c.° 3°. 2 Most trewlicho oon is pat pat is nongt depart id in in dodo noupor in wight

and vnderafcondynge and sucho oon is bigynnyngo and trolle of nonbre as he

soip. /ilso ho soip per© pat in oon is no multitude and pat is to vndcr-

stonde of alia pinges pat bop redact be he ncuer so diners. Ffor oon is

y-seido in many manere of wise as it schal bo y-knowc heer after. Also

for perfitnesae. For alio particulero pinges pe nhiche ouerlch is perfite

is hitsilf bsp perfite whan pey bep redact in to oon. For die holnosse and. perfitenesse longep to oon and to volte as it is y-aeide 11. Do Colo

and de Mundo, c.° 2°. Also for singuler dignite. For oon by it silf hap n 4 . a singuler boynge as it is y-scid in 11. Meth. c.° iij, pat pe cause of

oon and of vnito is oon esaonciallichc and first noblo and passynge rorpy. ■ c Oon and volte is y-take in many® vise as Alg(asel) seip. Son oon is synplo

and oba in oon by eomwhat.pat longep perto. Ora syapleliche is oon pat may

viee»

and ox as Sortes 1*5

1. So fB| LB li. ij. c. i. 2* TB is pat is pat* 3* IB i de celoj LB li; de celo; WdW I. de Celo. 4* So IB; LB 11. motaph* c. xvi. et ido algagsl dicit super iij Metha. Ci v. quod ca(m) est v m s essencialitcj Wdw ... as it is eayd in libro Mothaphorua caplo xv. And therfore Algr. sayth super iij0 Methaphonaa °a. xsr. That the cause of one and of vnifce is one essencially. 5. IB Algerj LB Alga; list of sources at end of Book HX, IB Algagsl. fuodPlato,

1b cubiecte as oweeto and white be}> in oon subataunco and body. In Prin­ ciple Phicorm, c.° 5°, Aristotil sei*) (Metaph. Dolta 6) bat son oon is

by hitsilf is sold in many wisor at pc nyddilj and

nay not ba departed as a poyntj and oon in nombre as singular; oon in ainplicite as beynge; and oon in alia holenes and perfoccioun as a cerde; and oon in matioro as alia bodilichc binges. Bar, and E(u)g.° 5°^ dis- tingucb 5 manor wise of oon and of vnito. Ffor many dyuera bingos y- gaderod togidres bob oon as many stones nakeb oon hope; and oon vnite is byndyngo and couplynge of dyuers parties of be whicho is oon y-made,

&b nombres bob oon bodj;. some by ioynyngo of male and female in geedrynge of children and so vif and housbondo bob oone whanne nan and woman bob tneyne in oon fleissh; and some by oonyng of dyuers kyndas in oon per- son® and bis is vnite of gendrynge and bttrbe and in bis vnite (beb) body and soule oo^.man. So pQ gracious vnito hab fouro diner sit ees. pa firste

1. WdS one in specyal kynde and shape: as Sortes and Plato. In san- kynda one in general kynde as man. And oxo in general kynde of bestys; LB et vxraat specie vel forma ut Sortes et Plato in homine. vnua genera vt hom ot bos in aiali (animall). 2. LB Bor. autca distinguit ix modos vnitatia ad liigenam v.; vTd'.V B and Engr. quinto dystyngueth fyuo manere wyse. S. TB in bis vnite be body and scale oon man; W in this vnytee the body and soule bon oo man. scale. |>e

(Lords).

&e Boxile is as

(i)s be volts of

solo and so ]?at

and to imito. as Ar(istofcle) scij> 5° Phico(: )• nought vnluersalliche y-clepod oon, as he oeifr.

im

in kynde, as ran is so of

But oon and vnite pat is j)e *,yelle of ncmtoe, is

but in noabr®, as A(ristotle) aei|>$ and is most

as it is y-selde 10 0 3°.

(c. iii),

and vndiuisible, and is fce

TB oon soulo a nd oon body in ouro; LB per charitatcm nultoran in domino est anima vna ©t cor vnumj MM follows 13. 2. TB as it is y-solda 4 Moth.; LBvt dlcitur iiij Hethor. ca. ilj; I?dW *• ^ is sayd iiij Methap. firsts manere euGrlastyngo God clone of die natiore and is nou^t oon- liche principal heed^ mad in Hia is no mi#t y-aedlM ^at may be chaunged.

JUKI so of Hia laat is ooa God in substauncc cocsetb. alio creatures, effectualliche and by ensample, as alio fconbrac) 2 cmep of con, as of i>o heed and wellej and to Him alle fringes befr referred as to fro chief ends, m ncmbi’cs befr y-dolid by the first vnite, frat is bigymyrnge and end#,

(frat) be oon, frat io God, frat is y-blessed dfrouten endo.5 Amen,

De Dualitate, Capitulna GXVII.

. Iff oon is y-do to oon franno comefr tweyne, and frat nombro is after oon first principal and welle of noumbre and holdofr fro secoundario place, as laid, seifr. And fria nembra hat to binariua and is infames among scan non for by fro nombre of tneyne wo befr departed fro oon; and so frio nombre

Is acomptad tokne (of)5 diuisioun and @f departyng. But Austyn in 6°

Muolcc seifr frat if fris nombre io to blame for he passefr furst fro oon, frame he is to proisynge for he ccmefr of oon, and neighefr furst to fro

Be Temario, Capltulm GZVUI.

The nombre of frre hatte ternarius and is y-gendred of oon y-do to tt/eyne and io most holy among nombres, for frerlnne io y-founde lilcenosse of fro holy Irinito. Efor as fre vnite of fre firste principal presentefr oon.

1. Scribal mission here in TBj LB non solum eot principimi prisma tan- quiS motor sed tanquig forma et finis et actus vliimus. Ei non adsaisoetur etc.; W follows TB. 2* IB maabres; MY7 samborcs; LB nuaorus. 5* TB bigynnynge and ende aa y be oon, etc.; WdW follows TBj LB sicut ad vnitatom primsm rasnoo nuneri resoluuntur rb idem sit finis mniua qul et

&» TB nombre is accepted tokne and diuisioun; Wd9 nombre is acountyd token snd dyuyoyon; LB Unde note dicitur esse diuisionio. in God.

glorious1 in nocbro of >re, as it is y-seido in li(bro) De Co(lo) and

Mondo, c.° 2°. For cuorich creature criejp and prcche^ $>e Holy Trinite,

and mesure, as it is y-seido Sap(ientia) xi. (xi, 21),2 Oon y-do to ^ro eakep foure, and nombre of fours hatte quatornarius, and ha)> t>at name of quadrats figure and square, as Tsid. soip (5.5.2). Quadrate schap end square is most stedcfaat and stable, and bitoknefc $>erfore most &e stable- nesse of al holy Chircho and stsdefastnesse of a crlsteno soule in virtues and scions and loro, pat he knor/ip wip alle seintos vrhat is lengpe and brede, 5 highnesse and depnos. And oon y-do to foure nakep pe secounde odde nouabro, pat is po nosibre of fyue and hatte quinarius. Ziaongo odde nostros pilke pat passep pro by Wayne is po secounde and ofte bitoknep hem pat puttep

De Senario, Capitulua CHX.4

Oon y-do to fyue makep pe nonbro of sire, pe which hatte Denarius and is po firsto porfito nonbro. (I)f pe eueno parties porof (bo) y-taken alio togidro pey cakep pe same nonbre and some, pat is nougt founds in a

1. So TB, VSiW? LB magnificaro 2. 5. So TB, So TB, ten byneijie eights and twenty. J>erforo c.° xviij01 Boicius aoip |xxt j)o noabre of sixo is a nombro Jsat rolowej) virtu; ffor he passe$> ncugt in

superfluito, nou$>er faylej) in la k and defauto, but holdeth the mono bi- twono euene parties and hafc no superfluytes nou$>er defaute. For in nonbre of six©2 halnendol is $*ro and t>e $>ridde tweyne and pe sixto is oon.

And sixe sijjos oon iaakoJ> sixo, and teles Jeto maki$> sixe, and Jades tweyne makojj {>e sane nonbre j and |x?rfore in holy writto J>is nonbro bitoknoj) per- feccioun of grace and of vertue.

Do Soptcnario, Capitulum CZX.5

Oon y-do to sixo, bat make)? scuene, and J>is nombro hatto septenarius

and is J>s Jiridde among odde nombres and tokneb encreusinge of seuene mancre grace b^t alway encrosib and perfiteb4 in hem Jut holdeb b© feib

of be most Verray Trinite.5

Da Octonario, Gapitulum OHI.6

Oon y-do to seuene meketh the nombre of eights, pat hatte octonarius

and comeb of twoye euone parties, or of tweie nesnbres of fours; or of 7 tweyne vnouene parties and odde, of fyuo and;of &ro; and toknsb be passing

ioyo and blisse in heueno bat ho schal bane bat hauo here the seuene manor

gif to of grace, b'ore euenenosso of myndo schal anextere to pa euenonoasQ of

IT LB libro l. ca. xviij; ferr follows TB, I, So TtdW, TB| LB Ham senarius continet in #e partem sui. 8# LB Gapitulum 4. LB perficit; WdV? prouffyteth. 5. LB boatissimej WdW most holy. LB Gapitulum of f parties or of _ .. . and __ _ Other of tweyne partyes other of tweyne LB ex duo bus quatwaarlje. vol ex good® dodes, and

of confeasoura, so Kt he be llehe la o*r# >lag##, and loye of vlrglnea

H loye of weddld folk, as oon aterre passed la elereaease, I ad Corinth xv (16.41) • And so fo euene and vneaene dedes hat here be# y-do. Ffor

IvmwwRRo f m c il lO n A 1 4 It 4» #a# p, y*a#*u#a 1 tkn4-p&t By&mP## A **A*%*rv»f»*tf**0*yr**g## Sw#pa K +*& 4 A KAp# T*Ai4 Are BwU#;a lohnls XV (14,E).

• ’ ' '• ■" . ■ De kooenarlo, Capltalu* CXttir

' Don y-do to eight# aakeh he noumbre of nyne and liatfce nonenarlua; and la ccmpouned of h^las hre, and la next to tea, and la bat oon bltwene; and toknop pa bllsse of pre lerarohlea of aungela of pe which# euerloh hah acord and llknesa to pa Holy Trlnlte and bep nerre to Sod than befr

a VlOfl lfe11

Be itenarlo, Capltulua c m n . 8

The ncsil»*e of ten passed nyne by oon and is ende, bounds, and mere of alle simple nombres, and first of alls h@ coapouned; and Is wox^y to presents Cure Lord Crist, Sod, pat la Alpha andcj, endynge and bygynnynge, and nou3t oonllcho blgynaynge and endynge of alle symple creatures but he loye and bllase of aungela and men. Also >8 noabre of ten Is pe fIrate

cihes ten maklp a parflt noabre, hat Is an hundred and passeh fro he lift syde to he right, as Beda selh-5 Herof it foloweh hat som notiire is digitus and some articularls and ataame ccmposltua. Euerloh simple noabre

1. LB cmm. 2.. LB cm . 3. So TB; WdW follows TB; LB begins new chapter: Cn* CBCVI. de dlulslone numeroroa. The discussion of even and odd rauabera 1# from Isidore, 3, 6. -to*

bynefce ten Is digitus. And ten Is be first artleulus, and be nexte Is

twenty, and bonne brltty, fourty, and so fozi». Coaqrositus Is cospouned

of digitus and of artleulus, as elleuene, twelue, and brltt^ne, and so

forb anon to twenty, bat is be aecounde artleulus, and so forb, brltty,

and fourty anon to an hundred. And ten hundred aaklb a bouaend,. and ber­

ime is be dlgnlte of be noebre of ten y-knowe and y-noted, for wlboute

ofte takynge of ten coaeb nougt a booaand. Hoabres takeb gretnease and

atwynne, as tweyne, fcure, slxe, and eights. So m noabres (ben) odds, bat say nciist be departed in to euene parties; for be cone partye is more and be ©bar lease, as In bra, fyue, and aeuene and obre suche, as laid* seltii. be miens noabre la dluldld in \>%& wise, soo is parted and s o b is imparted.2

That nouabre (la par) bat is departed3 la euene ncebrea alway, anoon to

oon bat is vndluialble. In bis wyae be halueadel of fours and syxty is

two and brltty, and half perof la aixtene, and half berof elgte, and half berof fours, and half berof tweyne, and half berof Is oon and Is In- 1

1. LB par alius Impar; idw follows TB.

dluiditur. quls alius eat parlter par. alius partter Impar. alius impariter par. at Imparlter Inpar; M B follows TB.

partlbus equle dluldl p(otes)t. n

lapar i>at la J>e nosabre fcat my be y-deleti euene atwyime, el&er half borof also my be dele* euene atwynne, W t such euen delynge eoae|» nouglit fulllche to o o b , as It fare# of foure and twenty; half berof ie xll, and half #erof la alxe, and half #erof la #re, #at nay nou3t be deled euene atwynne; and so the euene delyn^ erne# ncught fulllche to oon. Irapar la an odd# nonbre #at coma# of Bultlplloacloun of odde noabrea, a» fyuo and twenty and nyne and fourty, #at be# odde noobres and cua- pouned of odde (noabrea)1 and come# of ailtlpllcaclcun of odde ncabrea; am aeuene sl#e aeuene make# nyne and fourty, and fyue al#es fyue #&t make# fyue and twenty. And sou euene noebre la auperfluua and atm dlmlnltus. suparfluus la #e noabre #at ha# partlea #at make# a grettsr noabre #an Itallf, aa it fare# of #e noabre of twelue; (#e twelf#e)2 party# is oon, alxte la tweyne, #e four## la thre, #e #rldde foure, and baluendele la alxe; and oon, and tweyne, #re, foure, and alxe make# six- tene, #et passe# by foure; and so of auche noabre.

he Ruaerla Dlalnltla, Capltnlua CZXIIII.5

% e parties of a noabre dlminutlf make# lease noabre #an itallf, as1

1. laid. 3.6.6. Inparlter Inpar eat, qul ab Inparl noaero Inparlter men- suratur, ut xxv, xllx; qul dum mint Inpares nuaerl, ab inparltaia etlaa partibua divlduntur; LB Inparlter laper eat qul ab Imparl numro Inparlter nuaeratur vt .xxv. et .xllx. qul dluisl vt Imparea nuaerl ab laparlbue •t paribus dlulduntur; IB Impar ls an odde noebre #at eome# of aultlpllca- eloun of odde ncabrea, aa fyue and twenty and nyne and fourty, #at be# odde noabres and eompouned of euene ncabrea and odde; Wd8 follows TB. See Euclid, Book IX, Prop. 88$ If an odd number by multiplying an even

parties/ the twelfth party is one. See laid. 3.5.9. 3. IB does not begin new chapter. It fare* of fco noatito of ten, frat tmb $»re parties, fre ter*e party Is ooa, the fyue Is tweyne, and pe half Is fyue; and oat, tveyno, and fyue makep eights, pat la moeM lamas pan ten. And pe nombre of eights la such a noabre, and so bep many opera pat ooaep nougt fhllltiie of here otme par- 1 ties perof; as pe noobre of slxe (pat) M p pre parties: pe slate party perof Is oon, pe prldde is tseyns, Pe half Is pre; and tweyne, oon, and

slxe.

ray be 'mr'mrwwoon endob mm'Wm twpjpF In### # W*slxo mMmWWr and be gF f |F ofacr In #### elfdite* 1W w HFjp asmmmtm Bolce m * * * m* so lb* w Thou ## schalt # # m Wmm wm> W selde fynde parflte ncabres, ami pay bop soone acounted for pay bep sears and compouned In a ful stedefast ordre. And superflue noesbres and dlalnutyfe be vnordynetllche disposed and coapoanod of no eerteyne ordre of noabres. Vneuene noobres ben dluldsd In pis vise. Somme ben simple 3 and somae conpouned ami somae ben aene. The ayaple hap non (opre) par^f but oonllehe oon, oper vnltej as pe noabre of pre hap oonllche the prldde party, and fyue oonllche pe fyfpe, and seuene oonllche pe seuenpe. Such 123

1. Scribal omission, vt aenarlus hab3 enla llj partes) Wdw follows TB as above. 2. laid* 3.6.11, decern mills .c. xxvlll; TB fours score and slxtene bynepe a pousand ami slxe score and elgte and tveaty bynepe tea pousand; WdT? follows TB. In the Saplentla of Hrotsvltha, a learned Benedictine m m of Saxony (c. 932- c. 1002), there Is mention of a fourths “xxvlll, cecexevi, vlil alllla cxxvlll perfect! dimmtur." (See smith, I, p. lit, where this portion of her text is quoted.) 3. TB, JYdH euene; IS, Isld. (3.6.7) ellea# party &at is so ofte y-take pat It oak# eucne pe sdbb noabre. Com- k2

nyne, t'lftene, wane end twenty, and fyue and twenty. Pfor we selp pries pre and seuene slpee pre, and pries fyue and fyue siPee fyue. pe sene nombres semsnep aomdele hope eyaple and c^ouned in b o b wise, as nyne and

and)1 *3 vneoapounedj for perlnne is naught coBaune nosbre, but oonllche oon.

And is (seeundus)4 56 and eoepouned in coaparisOun to flftene, for in nyne and In flftene is an oper cosyn noabre oon, as pe noabre of pre: for pries pre aakop ful nyne and pries fyue cakep nil flftene.

Be Alla DSHslone Ihimerl, Capltulua CXXV.

And nouabrea bep departed and y-deled in anoper mner wise, ftr euerich ntabre is y-take by itsllf and lip ccsiparleoun, as oon, tweyne, pre, fcure, fyue, size, and opre auche. A nousbre Is y-take wlp o o b - parlsoun la pis wises pe nouabre of foure is double to tweyne and con- teynep ofte tweyne; and eixe is double to pree, end elgte to foure, and ten to fyue; and pre is treble to oon, and size to tweyne, and nyne to pre. And yllche grete nombres bep pilke pat e

1. "But here ... nombres" so TB, Rdf?; not in LB. 2* TB, wdf? nought oonllche by oon; LB non sola vaitate metluntur. 3. TB noabre of nyne is pe first# vnooapouned; EdW follows TB; IB nouen- arlua cnla dm comparetus ftterlt prims mt et ineoapoaltxia. Priaos here means "of the first order, prime." 4* TB And is pe secounde aiwi cmpouned; »d7; follows TB; LB Ad xv vero coaparatus seeundus ost et IneoapoaltUQ. Secunduo is "of the second order," ie, not prime. 5. So TB, Rdn; LB begins Chapter CXXVII, De secunda dluleione totlua nuaerl. See IeM. 3.6. for the following discussion. 6. So Rdw; LB equalcs. 1 Vneuena nosbrea ben fce acre and lassa, aa lire aM tweyne and fours and >re; ami generamche N more and lie lass# In eoaparleoun ben vneuene

and ao of olire.8 laaae noabre la conteyned In $»e more and la y-take

In coaimtrlaoun berto altii aom party berof, as bre to ffyue)8 and la eon- teyned In (fyue)1* 3 4 alb taele parties b*rof. A noabre bat batte multiplex oonteyneb ba laaae nombre tale# or briea or four albea; aa taeyne con-

bat la be haluendel of ouer bat la be bridde part of bra; and fyue conteyneb fcure and bat la be fourb# part of foura; a M ao of obre.

dT be laaae ncs*re; aa fyue conteyneb bra and tael# parties cuer b#b tweyne. And aeuene conteyneb foure and bre parties ouer, brlee oon. And

1. UB Inequalea. 1. LB, laid, give example of five and three. 3. TB foure; LB qulnarlua; $dH follows TB. 4. TB aubauperparclena; So T7d»; LB superpartlens; so laid. (3.6.8). 6. So TB; HdW follows TB; LB auperpaclentl. t w n e oJ>ep or mo, as %re la ooateyned la fyue and tsele parties #erof.

del or >e >rldd@ del or # foiu»e or M fyfte, e numbre multiplex superpar- tioularls1 omteyai* N lease nozbro of to and mm party perof, as fyue eonteynep teyea tieyne, pat mkep foure, and ooft party perof; as nyne

parties perof.

perof, and foure Is twyes conteyned in clleuene and pre parties perof, as tsld. selp.

Alia Dluislo Suserl Seeundua Xsld.,1 4*3 CapltaluB CXKVI.

t Hvmbres bep dluldld In pe prldde saaere In pis sleet some discrete, end some conteyned. A diecrete numbre is conteyned in discrete vnltees, as pre, foure, fyue, alxe, and so fwp. A numbre conteyned In discrete vnltees pat ben y-loyned, as pre. Is Vnderatonde In gratenease and quantlte.

1. To superpartleularls; Ids subsuperpartloularls; LB subpartleularla. laid. (3.6.11) euperpartlcmlarls. £. LB multiplex superpartlcularls; laid. (3.6.12) multiplex auperpertlo- nalia, submultiplex saperpartlcularls, meltlplex superpertiens; follows TB, LB. Passage was garbled In KS. of laid, (see variants on this section). 3. So W , LB, TBJ laid. (3.6.13) aubBultlplex auperpartlonalls. 4. The discussion of this third division of numbers Is taken from laid. and frla noobre is dlulded In lynaml, superficial, and In solid. #e nuabre lyneal bygynnep fro ben and la y-wrlte are*# and lyne anon to endelea?

In lengpe but also la brW* and la contoyned la lengpe and la bred#. A

In bred#;

Is y-ordeyned la pis else O and N qmdrant# CZ3 la #la via# and

fyue cornered la pla wise C D • N eerole noebre is y-aade pus O .

In a elrele wlae and aakep a spare al

slpea, for pis eerole multiplied by It allf alaboute make# a spare al

bep) may

I folwe a tie fulle. 12

1. LB celts all figures but says: Bt Idee figure sunt hoe ponende par example; spaces are left for figures la sow eases; Still follows TB. 2. The followlss passage (from "to bee" to "foist atte fulls") Is not Is LB; SdS follows TB; Isidore's order la not followed, nor bis wards "atte fulls.u LB la garbled here, toe. for wlfroute ncebre is not s (lettre) slliable to sillable in rigt ordre, dieetma, nouber M eonelusloun in nieses, nott^er M first*, mane, and

r<

end rlsynge, neuter ; help* of nouabre. a ' as be #el&. Also M # euerlohe ncabpe Is odde m, euene. tie euene noabpe may be deled euene

be y-deled vnder |» (dyuloloun)1 in leste and to amb: In lest

Ffor It Is dluidld, and J»ej*a may be none lasse dtolsloun ban In twele parties. For to N more party m m nombree Is y-delid, lasse nombre t»at leue$i; as It fare# of a tree #at Is hose to may parties, but #e nonbro of dlulsloune Is alwey more; and the cause Is, as ha eel#, for a gret quantlte may be dyuydad and wexe lease and lasse and bo ended Util,

orete quantlte. #e odde nosbre is kyndelltAe diuldcd In tweye partyes,

eon tyae to vneuene, more and lasse. And whanne #e nombro Is y-deled euene atsynne, if #e ooa party is euene8 #e o#er to euene, as wMnne eights Is y-delid In foure and fours, and tvelue In slxe and sixe; and so of o#re. And If ooa of euene dlulsioun Is odde, #s c^er is odde, as whanne sixe ia deled to #rs and #re, end ten In fyue and fyue, and four- tene to ssuene (and seueceX13 2 And so in euene dluleloun la nouit euenenesae

1. TB #e ease dymemloun and to leste and In moat; Wdl follows TB; IS sab endem dlulslons dluldl In minima at In maxima. 2. TB whanne #e noabre Is y-deled euene atwyane if #e oone party Is odde also (erasure to MS.) and if #e oon party is euene; l?d* whan the nombre le dealyd euon to tweyne yf the one partis la odde toe other la odde also. And yf the one -party is mien; LB Quando vero in partes dluldltur aquales si vna pars dlulsionie est par et rellqfua erlt per. 3. So Wdff, LB; TB emits "and seuene.15 nouHfcpe of tweyne, J»at ia prince of eueneneasa and fonge|) noujt euene tUulaioun; for It la coapounad of tiles oon and of #e ferste euanesoe of

tweyne* And If #e enene noebre Is deled In tweye partyes, more and lease.

If M oon party la euene M <*er la euene; as If ten Is y-deled, in aigte end tweye, #er In slxe end fours* Also If atxe Is dluldld In fours and tseyne, (and) eights (la)1 alM and tweyne; and ao of opra. But if pe fi oon oar tv. la • oddti nedae he nbai* In odda. fan) if tan ia v-doled in

e«i«ie end ^re, and elgte in pre end fyue; and ao of opr a. And it may be

neuero pat oon party of suche a dluloloun Is odde and the oper euene.

odd#; ae if pou deleat

And oon Is moder of plurallte and eauae of euene and odde; for if pou

eetteet oon to an odde noabre, nedea pou aakeat an euene nosbre, and If

pou takeet oon m% of an euene noWire, anocm pou aakeat an odde noabre. Also of all iioebres yaette In kynde dlaposlelcun about# oon and y-loyaed

togldres, oon la pe sayddel. As if pou salat oon, tweyne, pres oon y-do . . : " ' to oon oakep tweyne, pe ayddel bltwene oon and pre. Also if pou aelat

tweyne, pre, fours: oon y-do to tweyne makep pre, pe ayddll bltwene tweyne

and foure* Also if pou aelst pre, fours, fyues oon y-do to pree aakep ' ' " " a ' fours, pe Myddll bitweene pre and fyue. (And ao) of oper paasyng upward.

Of parties and special kyndes of euene nombre and odde It Is y-treeted

toforehonde. To make process# of all# pe gendrynges and proporclouns 123

1. TB In eights and slxe;sdi follows 2B. ~ 2. TB, RdH and; LB vt. 3. TB omits “And so"; LB St sic de allia? Wdw and of other. ful loose * perfore of

N * In noaUres It is tiard to fyMe lie oyduil, as laid, aei# (3*9*1), Top

Byddil in>ie siset take six# for &e lease and xii for pe acre and Ms

laid, ssip 11.0 (U j)oi

et Pooderlbj, C&pltulua mil.

propretses |»erof sprlage^ of lore of geeetry. Pfor as Tsld. selfr, 11.°

(U))?1 geaetrl la a seienee of aesupynge and aetynge and oonteyne)> in

brede, and femes end distends, gretnesee and hugeness#, and in figures and dluisleeM and nouabres, as hit fare)* in eereles, triangles, and qua—

1. TB sites Book IIJ dieeuselon occure in Book III. t. LB cm x . what by cause of $ie syaplo, of be whlche IsM. mkeb nenoloun and seib in bis wise: of geastrle is fours aanere (dlulaloun)1: playne, and gretnesse of noebre, and gretnesse of reaoun, and solidus figures. Playne figures ben eonteyned in lengbe and in brede and be* fyue In noabre, as Plato me nap. (Raolonal)1 2 gretenesse and noabre may be y-deled by nombres; bat beb y-knowe In arsaetrlca.3 54 The aeeure of irracional gretnesse and huge- nee is nought y-knowe. A M solidus figures ben eonteyned in lengbe, brede, and depnease. A M such a figure is y-clepsd cubuc, and la al yllche longe, brode, and depe. Of pleyne figures is many special aaner schap, as he selb- be firate is be cercle in pleyne foots, and so y-eleped olrctm- ducta; and in be ayddel berof is a poynt in b® which# all# be lynes bat cooeb fro be rouMneaae berof me tab y-fere, and in game try Jfet poynt hatte centrum. A M be cercle is in pleyne foot# bus O The quadrangle Is in pleyne and lib wibinns foure strelgt lynes in bis wise C 3 * Diate- gramcm la a pleyne figure in bis else Q . Cfrtogoniua6 rectiangulum is a pleyne figure in this wise IX . Hieoplexoe is a pleyne figure and strelgt ordeyned vMer be solidus in bis wise . be spare is a figure y-achape al round and is hereto be solidus In alle parties in bis wise # . be cubus la proprellohe be solidus yllche long, brode, and depe in bis wise gg . Chlllndrus la a square figure wlb half m cercle about# in bis wise D B ,6 Conoun Is a figure brood at oon eMe and

1. TB dymensloun; LB diuialo; Wd» diuysion. 8. TB omits "raolonal”; LB Magnltudlnes rationales; Wd: follows TB. 3. TB y-knowe in arsaetrlca we my know# the assure; ;?dH know#/ In Ars- aetries the assure; LB scire possuwae ... slcut Irratlowle* quarum aen- sure quantitas oognita non Imbetur. 4. Mo diagrams appear in laid. (3.11, 18) or LB; MdW follows TB. 5. LB Ortogonlua id eat rectiangulum figure plana eat Id est trlangulus et hab3 angulua rectus its; Wdlf follows TB; laid. (3.12.2) Orthogonlua, Id est rectiangulum flgura plana. Eat enim trlangulua et habet angulua rectum. seharp at >at <*er la $)ls wise A Plramls Is a figure y-eehape In |>ls wise ^ , wyde byne$ie and strelebt aboue. bis science vseb first be poynt, bat hab non party; for among alls bat ben aesured It Is lest In quontlte and cost In might, for It Is bygynnynge of alia lynes, and perfro alia lynes blgynneb and strecheb ami endlth berotte. In degre1 bis sclonce vseb be lyne, bat la a etrel8t langb* wlboute bred# and strecoheb fro point; for he blgynnep at a poynt and ende> at a poynt. Superficies Is brede and lengbe. Splasltudo —* plkkenesse — Is brede and lonsbe and depnesse, and ouerych body hap bese pre dyaoenslouns, lengpe, brede, and blkkenesse, ami byne(pe) pise pre alle corpulent aubstaunoe hap mesure, noumbre, and wlgt. And by art of tellyng and nmsbrea thow might fynde pe myddol in gemetre, for pe leate and pe mate y-ml tip lied makep as moche as pe mens makep y-@ultlplyed; as slxe and twelue y-multiplyed mkep two n2 and seuenty, as Ysld selp 11.° (ill). pa eercla Is a lyne y-drawe al rouml about# fro a certain poynt to pe same p

It allf and of non pat la wlpoute It sllis as It farop in pe cercle of

Heuene, pat blcllppeth alle and Is nou3t byelipped, and conteynoth alle and Is oonteyned of non pat la wlpoute. As Ysld. selp (3.12.7), as wlplnne ten Is euerlche nombre, so wlplnne pe cercle Is y-closed al maner schap

6* laid. (3.12.4) Cyllndms eat flgura quadrata, habens superlus aese- drouloa. The error has come, It seems, from Isidore, who saw a cylinder drawn In perspective ami did not understand the drawing. 1. LB secundo; so Is id.; lidw follows TB. 2* laid. (3.13.1) shows that the proportion referred to Is 6$8$:»tll. of figure In pis wise

al ping folowep pe i for Heuene Is round* In seha] dop all* po aterra*. And so

and trees, seed and fruyte eoa^i euerleh of oper and tornep in to beasllf ' ' ' ..." . ' '.. . * ■ .v >'■ . *^ia* So po splrltes of Heuene eooep of God. by creaoloun and mkynge,

- ' - " ' ' ' ■ . ' ■ ' ~

' ; ' . ; ■ ; ' . ' ■ : . ' - ■ ; - - ■ • ; ' and tornep toward God by dades of pankynge. So Aristotle llknep pe resonable soul* to a eerele by oauee of porfeeoloun perof and of diepwl-

•loan to fongo. Of all* pe figure of pe same lei^pe, pe eerele Is pa

pe soul# schulde It take by vnderatondynge and Inwltte (pat) God k Creator

' ■ ..... ' % ■ ' • and Maker* of all, and Is designed (alia) In a eerele. For am Trunegestus

- - . . ' '' : - - . ' " . ' . ^ . - '' \ " selp. Con gendrep Don, and bondep His loue In to Him wlpoute bygynnynge, . and splrep pe Holy Dost by pe gone. And pe Holy Goat Is pe knotte and

loue of eyper of pe Fader and Son*, for pe Fader vnderatondep Him per- fltellche wlpoute blgynnynge and louep vnderstongynge perfltUeH Hlaailf. pet loue streeehep to non oper paasynge Himself but to him pat vnderstondep and Is vnderstonde to pe Fader and Seme, of pe which* It eoaep N t loue

and bendep in Hlmallf In a eerele wise; and so pe same Is God and Easencla,

pe Fader stondyng and so gendryng pe tone and pe Gone y-gendred of pe Fader 1

1. tB planet** about#; SdW meuyth; LB planetaru# orbes In ee circularltur. , '-'I , ;* if Qod is intellec­ is Qod (' And ao in alia in ao And le eehyneh in eehyneh le 1 -M- follow / / is Solidus. is reatlas %d* %d* reatlas a l a a 1. triangle la the firate, for he for firate, the la triangle nought he misbre of he Trlnlte. herfore he philoaophre $>at hlghte Secun- hlghte $>at philoaophre he herfore Trlnlte. he of misbre he nought perfeeelouns i# in J»o personae of Sod, and bat |>e pluralite of hem paeme# paeme# hem of pluralite |>e bat and Sod, of personae J»o in i# perfeeelouns rebounded in to el$>er and is $>e Holy dost. And so it may be Knowe Knowe be may it so And dost. Holy $>e is and el$>er to in rebounded tual «wl voderatonde; and M loie by J»e Sons coaeji of $)e Fader and bended and and bended and Fader $)e of coaeji Sons J»e by M loie and voderatonde; «wl no where. And so he so And where. no 26**

Btrecche)) fro tweye cornerea to $>e contrary corneres; and by lynea y-draee the fjrue cornered figure conteynej* fyue triangles, and i>e slxe cornered figure slxe, and fre seuen cornered figure seuene; and so of $>e ofcre, as

Boys. (s#i#) 11.® 11,° Arsmetrlo, c.° vi°. But $>e triangle may nou3t be so ydeled in obre figures than triangles in bis wise.1 bis figure is so granted * of bred bat ©bar figures beb resolued and deled In triangles

And for bis figure is y-bounde to none principles, nouber tokeb (of) ob#r figures bygynnynge of brede, berfore bis figure is ydeled in itself, as he selb here.* 23 Ami non ober figure may be bybou^it bat hab nougt blgynnynge and principle of be triangle, (bat) le bygynnynge and element of ©here figures and seh&ppes; and pat is yknows in noabres, for be nombre of foure Is ctsnpowned of bre, bat is a triangle in noabres, and of oon, bat makeb foure, ydo to bre. Pfor oon hab ble dignlte, bat he conteyneb in hitself al be virtu of be noabres bat comeb berof, nougt in dede but In might and virtu, as Boys selb, 11.° xl,° c.° xliil.°4 And so be nombre of fyue is compowned of foure and of oon, in stede of a triangle; and so it may be sohewed of al ober numeral figure, for alway eueryoh nombre is y geidred of a triangle figure, as Boya. deteraynep pere in teraes openllche, and settep ensample in figures of fours, of fyue, of sim, and of seuene, and of many opera. Also pe triangle figure Imp nouper ainguler proprete,

T. LB Ms here "nisi in se ipsaa”; Ids follows TB. 2. IB figure appears in margin; WdH figure appears in text after "prynced® (for which TB has "prented"). Of the triangle LB says "in tres anim trlan- guloa dluiditur vt patat hie (spaee for figure)." # 3. HdB follows TB? LB Ipsa' vefo quaa nullla est prlnclplis obnoxla nequla 6b alia latitudlne sumpelt inltium in se ipsaa soluatur vt dielt Idea ibidem. The sense of tills seems to be: "Triangles, whieh are responsible to no other unity and make their area from; the combination of no. other fora of super- - fidea, are units in themselves." ' - - 4. LB liber i|. e xvllj.; ,dW follows TB. ffor of euerieh o$>er figure, acme syde m y be M chief side of N triangle, and ao vpen euerieh ober figure may be rered a triangles for euerieh o>er figure plrtuaydale, hat hah la It sllf he schap of triangle, conteyneh In it sllf as many triangles as h« chief side conteyneh eorneres. As If a quadrangle is y-setts for h» chief ground and syde, there asy arise a figure plrosydalls hat conteyneh In It sllf as mny triangles as he quad­ rangle hah eorneres in it self in his else. Also If the chief syde or basis Is fyue cornered, he triangle plraals hat riseh may presente fyue triangles vpon jmt basis, as it fare# la a plraaydale figure hat my be basis of he figure plraals, as he selh.1 And In he plraaydal triangle hre aanere triangle may be y-founde, as he corners herof ben hre In his wise.8 And so h« dlsposieloun of God semap wonderful In all hinges, and naaellche m numbres and figures. Of ohre figures, hope of noebres and

gsaetre, it Is seaellche now to cesse, for difficult# and dyuerslte of endeles aany figures, hough pe consideracloun of alls be ful profitable to h® lore of dlulnlte; aa In he quadrangle, hat la most solid and atede- faste among figures and numbres and is square and presontep h° lore of he Gospel, hat hap stedefaatnesse In he fours parties of he world, as

Beds solh super gen(esls). A corner hatte angulus and is he touchings of tweye lynes hat toucheh elher oher and Is he oomins subjects of many figures, for alia he forselde figures beh temyned vnder dyuerslte of

angle hatte rectus angulus and somae obllquus and (soam) reflsxus and 12*

1. So TB, KdRJ LB has mention of hexagonal figure as another example at this point. 2. The omission of these figures, which would Involve perspective, lends support to the supposition that Bartholomaeue did not know its principles; it Is possible that he did and that later copyists did not. see note and drawing of cylinder on page 21. Boama acufcuc and socsae obtusus. And most virtu Is In be angle fcat hatte

reetow, for Jjorlnno al po vertu Is yatren^ld — i>ut la in &e lynes Jiat

coaajj fro be basis to be angle;1 and be vertu Is y-strengbed by concours

and aetyng and touching of lynes, as It fare# In be yge, bat oonteyneb al blng voder an angle. For b@ (lygnes)8 bat eoseb from be bins bat Is y-aeen

strelgt to b» yhe aakeb plroee of be whlehe be poynt 1# In b° blak of be yhe and be brode ondo In be bins bat is y-selo; and bilko bemes beb y-angled

in be myddel of b® blak of b« yhe, and by b# angle of bat plrame be sight

la y-sbhape, as be auetor of perspectlue selb, loko tofore ll.° ill® (Da

natura visum, and in Hbro ,v») D# materia vel nature oculorua and sen(lo)r.

nombres and of figures. For as b® cercle tokeneb be soule raeional, (and)

the triangle be sail# of (lyf, so b# quadrangle tdteeb N soule of) fellnge.

Ffor as be quadrangle oonteyneb taeye triangles if a lyne Is y-drane from

teyneb In itallf tweye triangles of might and of vertu. Ffor b» soule of 12*4

1. This portion Is set off by dashes because, while TB and BdE have not marked It off, LB has It In parentheses. 2. TB highnesses WdW hyghnesae; LB tern radii qul llnealiter venlunt. S* TB loke tofore U.° ill0 De materia vel nature oeulorum and sen(lo)r* be parties; WdW Loke tofore llbro. 11). De materia vel nature vlsus. and llbro .v.° De nature oculorua awi 8#n(l@)r. The party##; LB Quere supra 11. 11). de nature vlsus. et in 11. .v. de nature oculorua. Partes Itaque. 4. TB and WdW wait the portion In parentheses; LB sis elreulua signet anlaaa rationalem et trlangulus anlaaa vegatabllea sic quadrangulus anloam eenslblleo. •oule of lyf and notigt agentiard. Ami so of ot>ro figures be# dyuers priue resouns and spiritual (#at) y-take In spiritual and corporal be# aoorded vnder #ese figures, (And so) ben conprehendld resouns of manures and of welgtea. As laid, sel#, 11.° xll°, o.° penultlao,1 a aeaure Is son #lng in his mnere y-mete <*er M s duryng by tyme; ami assure Is of

body, o#er of tyme, o#er of spaee$ and of plane #e aesure of body la as

^ asn, of trees, and o#re bodllyohe #lnges. In leng#e and in brede,

for eusrlebe body ha# his owns dyaenslotm and assure. And #at is propre-

tarlus. Ami #e leste aeaure is eoclmrlum, and is half a

vegi# nyne huolea; and such# #re make# a conoula, a drag®# ami an half. And #e wlgt cla(t)us conteyne# ten dragaesj

eolna and conteyne# xil dragaes. (Cotula)1 2 la ealna and ha# #at name of

partis of sextarlus y-deled euene atweyne and hatte cotula, emd ealna

weyo# a pound#; ami such# tweyne mke# sextarlus ami Is ## aesure of

#erfore. Conglus ha# #at name of congregamlo, gaderynge, o#er of crea-

1. IB, M S run text right on here; IB begins new chapter: Ca. CXXVI, de aensurls corporum aemnirabillua. IB, Id* connect Isld. with the fore­ going passage, citing Book XII, but IS hes chapter heading and: Est autea aensurs vt dlolt laid. 11. xtrl. o. penultlao. The discussion following Is from laid, 16.E&. 2. IB concula; laid, cotyla; LB cotula; M * conoula. for to be holds>o

Is a

for It is

sake* two and twenty sextarlus; and Is *®rfore figure and tokens of N

pe ■» and sterres; and

ater, and fcules; t>e alxte days

of M londe, and man. And so 1

to laeob, of him com al #e poeple of Israel; and two and twenty boofces of

H olds testament; end two and twenty lettree of .a.b.c. by be tislche al

for it is a Ysld. selb (16.86.10).

and an half; and be for

•aturn. Is y-cleped j V ’' rare b» Bess , pa

twelue sextarlus, as Ysld. selb (16.86.11). Is In fletynge lUnges aa (ohorue)1 and e$ht In druye *»lng@8. Amphora ha> i>at name of anals, handle 1, by M whlohe (it la) y-houe hider and #lder, and hold## of Whet# o#er wyn# #re modlua of Ttallo. Cadis is an amphora Jmt hold#

#rles vrna. frna la a assure #at aoaae men cl^l# quarterlum; and propre-

Heh# to spake vrna is y-ordeyned to do #erlime axen of tied# bodies, #erof

#• poet# spekl# and aei# #at he ia haled #at ha# nought vrna. irtaba is

• ■eaure among #e Bgipeiena and hold## #re aoore sextarla and twelue, and ha# #at name of #re score langagea and twelue of naeleuna bat oceapie#

## world#. Oomor la a meaure of fourty medium, aa Yald. ael# (16.26.17),

©#er it la a meaure of #re or four# modlus, as #e glo#a eel# super Bx.°

0.0 xvi (Exodus 16*16-1#). Chorus ia a meaure of #ritty modina and ha#

#at name of coaoeruacloun, huplyng, for #rltty Bodies in don huplo asms# a Util hulls, and la #e charg of a eamele. Huo vaqg Yald. 11»° xfl.°

(16.26). Also ber be# many o#er nanere closures of #e whlche #e names ben y-aette in holy writte, and nougt wi#outo grate cause of prime and alstlk

eleped acetabulum, as Yald. eel# 11.° deelao (20.4.12).8 Ampulla is a lit el meaure of liqueur# and ha# #at name as it were ample bulla, a large bulla) and is llehe in rcundneas# to belles #at some# of #e foae of water

1. TB coiraj WdW follows TB; LB chorus. S. TB, WdW cite 11.® Xi LB 11. xx; passage occurs in Book 20. -ai­

ls & vessel

lapldlbus. Arche la a

$*t name come# #ls word archonu®, prlusts, #et Is sllllehs y-kepts vn- knowen to sultltude of mem. Am#iors is a eerteyn assure and he# that neat (of) ansls, hotidelea, as It Is y-selde tofore. Betas is a aesun

CatMnum Is an ermine vessel ordeyned for mete and for dryidce and Is better y-seid in #e neutre gendre #an in #e aasettlime, as sallnua, a ealere, as Yald. eel# (20.6.6). Cacabus, a caudroun, is a vessel of kechene ordeyned for dyuers vse ami to se#e fleissh Inne, and also *e same vessel (hatte) ootule.1 Cadus is a berel and eomteyae# #re aodlue, as it is here seyde (80.6.4). Calatbus la a basket y-made of splyntes to here flges herlnae. crlbrua is a syue, rounds wl# many holes, and ha#

N t name as hit wore curriforum, beryngo hinges hat ronneth, for wheto and ©her some renne# herlnae; for in a syue come is y-elansed of stones and of seal chaffs. data la a Util hucche; and of hat name comeh a dymynutyf, elstreUa? and hah h® names of ryndss, oher aplyntres, of eases

©her of parlsch of he which# it is y-wove and y-wrought. Cophlnus is a vessel y-w«ie of 3«pdes to beren drltte herlzme, as It is y-aeyde in i;, TB, WdW omit "hatte"; LB nominetur. IB, Kdil cocula; LB cotula. Psalmua (80.7), Manus elua In copMno aemiepunt. (C)olata bep vessels

Mobe cleped eyllowb ee Yald. selp (20.4.7). Glabra be> vesseles for

as It were.a bote. Coolear, a spoone, la a lltll Inetrument of pe aeaure

eleped dlaeuabentea and hauep pat m m of dlsaue. Dollua, a tonne, Is r an holow* vessel and hap pat name of dolando, hewynge ober thwytynge, for

Ealeadiua Is an c^er vassal and oonteyneb half a eadua. Bnoforua Is a vessel and bold# wyne, for eno Is syne; perfere It la aside, vlrtitur enoforl fundus (sentenflla)1* 4 nobis, as Ysld sal# (80.6.4). Fflola ha# M name of glaa, for glaa hatte file In Gru, end la a Utel vessel wl$> a

colour. Phllaterlum Is a Utel vessel of glaa o$ter of crlstal In be whltiie holy rellkes ben y-kepte. Also #e pereheeyn la p* which lewes vrlten >e laws for to blholde holy la y-ol##d phllaterlum, as it Is y-

1. LB ferramentl quod vulgo clllonea vooant; TB hree bat ... cylleon; WdH.thre that .. Cllleon. 8# LB dlstlcon antiquorum; RdW olde dyatynecoun. $#' Martial, Eplgwma, 14.181. 4. TB alnna; laid., LB, ItoYi nontentla. ••JUIe, Mletmnt eiua philat®pia sua (Matthew 23:5). Plseus la a cmayn tok op a bagge In po which* #e esehetour and rente ptderers do$> |»e goes

acoeplt Chrlatus eaplt flaoua. Flscella la a litel euelong arlbbs ouber a panyer y-eeue w # aoale 3erdes of wlbye <*er of perache, and y- glewad ou|»r plcched as waa be veasel la be ehlehe Moyaes was lime whanne he was y-do In be ryuer. Qauta la a gret heuy belle, holow bolls and depe and hatte gauata as It were eauata, holowg, here .g. la y-sette for

as Ysld. selb (80.4.11). Oajofllaelua la a bneehe In b# wMdh la

and hab bat name as It were archa gasarua, b» (bucehe)1 of rlehesse and kepynge berof; for kepynge la fllaxe la (fi-uew, as Ysld. selb (20.9.1).

And so gagofllaolua was an Imcohe ob*r a hous kepynge pa eoeaune offrynge, as naisa2 kepep be offryng of kynges and eorban of prestem (as be gloa© selb super Regia Iv, 17:18).3 Ydrla Is a water vessel, fra* water hatte

1* TB whlche; r m coffre; LB area, which Is translated ,laio«hen at the

2. So 5EB, Rdn; LB eaisae; see note In appendix. 8. TB, Wdw wait the port lea In parenthesis; LB vt dlelt glo super 111) 11. Regua. 4# So TB, WdS; LB adds "Aqua dloltur la latino." This la probably a scribal addition. In response to the Invitation In the last chapter of MS. vasculua ex vlalnlbus slue canals arundlnls contextuo fnmtlWs deferoadls deputatua. Karoulua eat conslmlle vasculua ex (vergls? MS. not clear) albls et flexls artlvlelallter preparatua. (Eahlstrua Is vessel made of wicker-work or rather reedy canes for carrying fruit for estimating. Karoulua Is a very (withes?) skillfully prepared. ... fTor In eucbe vessel J>e oyle was y-kepfce to annoynte klnges and ppeates,

as Ysld* sel$> (20.7.6). Labes Is a vessel of teas to se^e flelsch >er-

Infecteb ofte mete $iat Is loage y-kspte per lime.1 Loculus Is a purse In pe ihlcha moneys is y-do and y-kepte as it were in a prluey place and

Mtte also aorsopimo, as Ysid. seip (20.9.3-4). Itorsuplum la a bagge to to tone moneye and pat name (comap) of the Oruwe word oorsupa. Itolgarlin is a ailkyng veasel, as laid selp (20.6.7). Koala Is a grate bolle, deep and round#, and was so y-oleped for all# round# plngea ben y-cleped (so) among P# Greece. Hole is a lltel belle and bap pat name of (a eity)2 of

Campania pat la Kola, pare such a belle warn first y-fcandej and Is Util and sownep; and hatte tlntinabulua, a# pe bells pat Is ofte y-honged aboute pe nekkes of houndes and feet of foweles and brlddea, as fitter selp. A croltke hatte oils, for water boylep perlnae whanne fyre is per vnder and vapour paasep vpsard; and pe bolle pat rysep on pe water and durep by suatynaunce of pe wynde and (air#)2 hatte bulla. Parapsis is a square vessel wip fours sydes yllehe. Patena (is) y-aade of dispansls and pafcentibg lands oris, as Ysid. selp (20.4.10). Patera is a manere viola ami hap pat mas for ws drynkcp ofte perof; for per brerdes ben euene and atwynne, as Ysid. selp (20.5.2). Poculua hap pe name of potando, drynkynge, and eueriche vessel pat m m vslp to drynke of hatte pocultm.

Patella, pe panne, (is) as it were an open ertidte, for a panne hap an openers soup pan a erokke, for pe soup is as brode as pe botoao; and Is a vessel of bras or of led# nedeful to many manor vse. A bacyn hatte

TI LB nisi ab eia citlua extrahantur; TB. Titi” omit this. ' 2. TB aote; Mv cyte; LB eiuitsts. 3. TB glrej LB vento; SdS ayre. peltil* and ha# #at naaa of pallia, -tiie akynae, for perlnne ofte Is y- aalsshe #a skynno of foot© and of honde. A boxe hatte plxla, and ha#

#at m m of buxua, boxtree, for #erof ofte a boxe Is y«aade} for N tre

#at we clepl# borne $>e Qrees elepl# plxlx; and boxe Is y-mdo nos of metal

saua and to bare lettres, electuaries, llquorls, ponder, and oyneaentea.

Qulequllarlua is a vessel or euerleh $ilng In #e shlche coddes hnUtes o#@r eml chef (be#) y-do and y-saued. Sartago^ #e fryyng panne, ha# #at name

water and quenche# and elensl# #e same and #rose# vpward #e water, am laid# sel# (20.1.9). Rapatorlum Is a vessel In #e wMche rape# be# y-kepte or y-sode, as he sel#.1 solpIm, ia cuppe. Is a vessel of tree, of slluer, o#er of golds of #e shlche we drynke# and walssohl# cure hondes. A boket hatte sltula for It aeorde# to hem #at ben apurate to drynke #»rof, or for It trarste# water; for how It fonge# water and now It sohedl#. For while o boket Is y-empted, ano#er Is y-fllled. Slthariela Is a begge in

#e idilche #at weyferynge men lede# breed and o#er #inges #at hem node# la

#e way. A (i&skote)12 hatte sports perlnne Is brede ybore and o#re plnges pat node# to housholde and he# #at name for ofte It Is y-aaade of gerdes of

• aohrob #at la sportus. seortella la an oyle vessel and he# pat name for

It Is y-sade of leplr. scutella Is a dlmlrmtyf of scutum, a Beheld, for

1. Reference not found In laid.; A3 vt dlelt PnpenC?) — abbrev. not clear. 2. TB cuype; WdR baskette; LB sporta; laid, sports. H Is Uebe to a Util round sehelde, as TsM. eelfr (80.9.4). Sarinlua

Sallnua is a salsr, as laid, sei* (80.4*2),

a vessel si# fours feet is ayseleped trlallls.

Is a

is 1* vile

as Ysld. sel* (£0.6.7). Vrna is sspbOTa It is y-seide

(16.16.1)

Ds Mansur is, Capitulua CZKIX.5 31*

1. LB vt dieit Coast.; Wdl follows TBj laid, has only litres ab utero.1' & 7B, RdR phisolagia; LB philolagie. 3. LB Ca. CXXXII, Do Mensura Spec11 Looalls. in brad*. In highness*, in depnesse, and in weight*. And so our* grate 1 ande and aesured al J)Q wyde world and deled *a (parties in) prouynce, and preuyase in regiouna, (pilke) in place, (|iiike) in teritories, and teri- toriea in feldea, (pllke) in eentorles oper conturiea, and pilke in

to pe lest*. An vnche is pe leate party of aaesures of feldea* And vnela contoynop pro yncho in assure, and pe hand brede fours ynches, and pe foot*

and ton feet.*

.xl, c. d

is sixty foots Icmge in euerlche sid%

istae of lun(ctue)*

hep many oper manere meaures of pe whlehe we speklp noagt at pia tyme, but it la to witynge pat pe stadlai fold conteynep slxe scor» pans and fyue. 12*4

1. LB partes? TB, RdW omit "parties in.” 2. WdW doyes erthes; LB has no oorreapondlng words. S» LB pasaus xxl pedes x; H

Centupla la a feU of two hundred lugereo and haddo hat nano of an hundred

holdoh alvjay ho flroto nano, as Yuld. colh, llbro xv° c.e.penultIno, De

toe he Letynes elepeh (hem) allllnrla, he Drees stadia, and Prenaehe mea

leucas, hG Egipolens algnoe, and ho Pops poraoongaa; and no eondre, ffor

He telloh

selh (15.16.2). A wey is a space In h® whlehe cartage may met# and hah#

' hat name, via, of vehlculum, hing hat beroh, for horlnne ccmeh and meteh

atone, euene and peoiblo, and comyn to alio men, and fro rthoute stoppyngo

and greuynge, no ho oeith (15.16.6). he prluete wey longlh to nygo tonne

end is sehort and ny3 and oft# y-growe wlh gras for selde of feete and is

bysette wih trees on ether aide. Agger Is an huple of stones or a token®

it TB hat conteynep twenty housend fete; LB qui constat ex pedibua xx ailihus; KdW follows Yli Isld. (16.16.6) qui constat qulnque mllla pedlbus. -40-

la tie hlhe way, and histories cleplj) such a way Imygtene wey, }»erof It Is

(salde), Qualls sepe vie deprehensus in aggore serpens (Virgil, Aon., 5,

273). Iter1 Is a wey by t»e which a m n my go whlderward bat be sole. And

hard to passe. Seaita is t>e ayddll of be weye and hap pat name of seals, half | and seaita Is pe psp of men and eallls Is pe pap of bastes, slide and

bypapea In feldes and hauep pat name for pay ledep to pe m e m way. Dluer- sua Is n bondynge of xroyea and ledlp to dluerse place. And diuerticulua Is a benohlngo bysldos pe wey.12 Blnarlua is pe blgynnyng of twoye weyes, af pe which® oon lip

cross© bep y-sette In sutiie weyes pat pessynge men cay knowe nheper noy he echolde take. Cooplta is a place per many voles metep, as pm or fours, and is perilous place end doutooe as blnarlma. Ambitus (is) a space be-

ordeynod for a wey aboute nelghebours place and hap pe name of clrcunr eundo, goyng aboute. Orbits is pe form of a mole pat makep a deeps fore in pe syndynge and tredynge aboute. Actus is a place pare bastes ben ofte y-dryue and is slider and fikel. Vestigium Is pe fore pat leuep in pe

1. TB Iter iteneris is a wey; W a iter itener is a way; LB Iter nerls set via; laid. (16.16.8) Iter vel itus est via. 2. LB vie publics vel prluate; TB, BdW omit this. 2 w(y)che or

N leoee

e e

3W»° C.°

a Be Ponderibus, Capitulim cm.

as Ysld. selt> (16.25.1). Ffor )»« might of kynde 3lueh to alle bocilUche

hinges here owe wight, and wights rewleh all#; herfore weight© hah# h#

name ponduo, of ponendo, settynge. Ffor weight# matte# alls hinges in her

owns place, for weight Is nou3t elles hat fondynge of a hing toward him

owns place. Tweye hinges aakeh weights, ligh(t)nesse and heuynesse; and

eo lightness© in motile matlere aakeh vpward and reateb nought ar he erne

to his owne pise#, j ar he come to his came plai

. -

reateh nought ar

by here owne wight. And so al of

llghtnesse, for he party is et

ar he

herto. Also for

1. beestys; IB sic IsaSl- 2. S. 4. LB Ca. oxxxlll. Be of lisshtnosse, as toesrd M myiAll, Is cause of

113t it la y-f

la al one; for fringes fret eouefr

and BO light and ,al&ht. b«* dluWld aa bit

XT(1)° (16.26.3) laid. aal» fat a .sights halt.

cosynUche, fro frlng In fre Cliche a soai tyse fre frlng frat is y-weye; and sob tyae

hundred and talentus. And (of)

Utel coney, for he stondofr euene y-eeye by a ben fra frlnno frat Is y-weye Is In fre ofrer;

heuy belle hette (M,£5.6). And laid* eelth (16.20.7). (is) Jje fourtia parte of ealculua for It la ao litel |mt It Quadrana weye$> $>e four$ie del of an vnee and hatte quadrana In Hebrew.

Clclua In Latyno hatte (sleel) In Hebrew and wele# an vnce among hem. And among N Grees rlgt as among Latyna alelus la $>e fourbe part of an vnce and half a abater and weyep tweyne dragmes. In holy wrltte sldus la an vnce, and the fourpe part of an vncla among naclouna. Vncla hap pat mme for he oonep and byndep al noabre oi welgtea, and weyep elghte dragaes, pat

1* foore and twenty aerupulea, pat la y-take tot laweful weight#; for by pe noabre of the scruples perof pe noabre of houres of day and night ben aeounted. For twelf voces aaklp libra and la perfore aconnted a perfyt welgte, for perlnne bep as (many) voces as monepes In pe 3#ere. Libra (la

y-selde) as It were leberata, a eaudroun, for hit eonteynep In It allf all# pe forselde welgtea, as Ysld. selp (16.25.80)• Blllbrls welep twele libras

and la double libra. Coma weyep am hundred dragmes and la a name of Gru.

Talentua la aeounted pe gretteste weights among pe Grees, for (as) noplng

la lease pan calculus oper aaals, for as oon la In nosbrea ao calculus Is

In welstes, none sel3te Is more Pan talentua. But pis weight is diners

among naclouna, for among pe Romayna pe talentua weyep pre score pound and

twolue, as Pll(nus) aenep, and pat twele talentes weyep two hundred pound

and foure and fourty, pe talentua Is treble: leate, mens, and aoste. pe

lest# la of 60 pound, pe mene of seuenty pound and tweyne, and pe moate of

seuen score poundof and pat was talentua of aelntuary. Centenarlua Is pe

name of a noabre for It eonteynep an hundred pound, and for pe noabre of 1

1. TB vyfe quadra ns; S'dW follows TB$ LB Quadrana quartampartea vncle ponderat. 2. TB quadrana? so WdW? IB dodruna; laid. (16.25.17) eodrantea. 5. TB slots; RdH sicca? LB sleel? Imid. (16.25.1#) elsel. 4 LB Km; laid. (16.85.21) mine; MU, TB coma. 6. TB, M W pllnlua; IS, laid. (16.25.22) Plautus. 6. so Idii, TB? IS oelta "aM pe amte of semen score pound#" ? Is id. (16. 85.83) contun vlglntl. am hundred la perflte $>e Rosmyns ordeyned a weigte of &at name. Sue vsqg o 1 lalS. 11. xv(l), o. (xx)lll Da ponderlb3 at aenaurla.1

1. TB cites laid. APPENDIX %

1# ISIS* • . - . . ' : Isidore or Seville, to whom reference Is made In many places throu^out this text, is identified by Cajorl (18P6, p. HI), died out. About one century Seville, In Spain, wrote an

and of Casslodorius. Part eT; He gives definitions of technical terms and tiielr etymologies; but

divides numbers into odd and even, speaks of perfect and excessive numbers, etc., and finally burets out la admiration of number, as. foXlora: ttek^MBir oueber fro. all thu,s», m d everything toes

z-=s^z;,=.-=z'?L=': r = “,? later encyclopaedias and its influence upon mediaeval tbo%#t me

In science. Independently from theology." (Barton, I, 471, 472.)

1, Isidore*a source material. Isidore has the following note on the authorities la the science (5.

Be Avotorlbvs oita Kumerl dlBClpllnam'apud Graecos prlmua Pythagonm autuaant con* scrlpalaac, me delude a Hleomaeho dlffuslua esse disposltaa; qua® spud Latinos prlmis Apulelus, delmie Beetles transtulerunt.

1, For ps noabre of six# pat Is perflte. For a discussion of perfect makers see p. 12.

2, Aristotle. (S»4*32S(1)) The following account of the man and his Influence Is taken from Barton (I, 127 ff.); this Is not Barton's whole account, nor Is the matter taken la his order; it le, hoceter, verbatim. Aristotle’s influence, for good or evil, in every department of knowledge, was so tremendous that a good history of Arlstotellanlsm would include a large part of the history of •elsncc and of thought down to the eighteenth century. Disciple of Plato. Teacher of Alexander. In 336*334 he founded in the Lyceum of Athens a new philosophic school, the so-called Peripatetic school. One of the greatest philosophers and scientists of all times. Aristotle Is - 47-

eoooentary on them which has aaoumlatea 1 shall not attempt to dis­ cuss Aristotle and his works more fully here. ' ' ' ■ . - 1 ' : gt Da nulf (I, Ibn-Slzm (Avicenna, 960-1037) theologian, end a physician* eventful life, he managed to . ■

« philosophic encyclopaedia . aaties, and Metaphye title Sufflolentiae. - 3, Algasel. Barton (I, 755), considering the m n frtm the point of view of the historian of science, has this (la part) to says Al-Ohazzall, (1068-1111). The greatest theologian of Islam end

vastly ooro important for the historian of religion than for the historian of science, yet the latter must consider It If he would understand the development of Muslim philosophy. Algasel has exerted a very great influence upon Jewish and Christian scholas­ ticism. Dm ffulf.(l, 224), writing a history of philosophy, says (In part): Algasel or Algazsall (1068-1111) la the moat Important of the theologians who opposed the philosophers properly so called m the name of Mohomaedan orthodoxy. In his chief works, The Destruction of the Philosophers, and the Benovatlon of the Religious Sciences, he rejects as heretical many solutions defended hy the philosophers, particularly the eternity of the world and the procession of the spheres, in place of their rationalistic science ho would oubstl-

speculatlon provided It be humble, submissive, and that in any case it does not claim to suffice as a foundation for the truths of faith. Endowed with a profoundly mystical temperament, Algasel studied all the degrees of that intuitive science which Is the mark of asceticism and faith, while ordinary knowledge la the work of the senses and the reason.

6, styntynge state, quite, and reate of alle vnltees. fheon of Smyrna, avoiding to Heath (II, 279), contains "the explana­ tion that the monad is Uhat which, when the multitude Is diminished by way of continued subtraction, la deprived of all number and takes an abiding position and rest.** -48-

5, Iff oon Is y-do to oon. The double f In this word is explained by the custm of the scribes of beginning a chapter with a large capital letter and capitalizing the first letter following (in the mame word) with a common els* capital. The double £ represents s capital. - . . ' J It :'.r.. 6, Au#tyn* Consideration of St. Augustine (354-430) has been undertaken froa the point of view of the theologian and the philosopher; Ssrton (I, 383), however, states that he does not 1mm of any eompreheaaiv* study from the point of view of the historian of science. The reference In the text la sloply a cotter of number symbollam, Augustine (Sarton, I, 303) was ’’one of the greatest Fathers of the Church. Two of his works which belong to the latter part of his life have become classics of the world literature: the ’Confessions* and ’The City of Sod1.” These works had much influence on theological writers in the Middle Ag@#* - . - " \ ^ . ' - ' ' _ - - V'\:' #, Bolelus (elsewhere Boys). The following note is tsken from Bell (p. 37). Boothlua (475-526) was the last Homan of note to study the litera­ ture and science of Greece. Bis works afforded to medieval Europe some glimpse of the intellectual life of the old world, and thus

fourth books, together with numerous practical applications to finding areas, etc.; to It was added an appendix containing the proofs of the first three propositions. Be laso wrote an arith­ metic. These remained standard textbooks for some centuries; they in the middle ages. Cajori (pr. 67) has this to say of As a Scholars, but a Lniputlem by the side of Greek masi

the arithmetic of Some of Boothlua1 arithmetic.

I, For in pe noaore of sixe haluendel la pre. m ^ The conclusion arrived at may not seem well founded, since the reasons given are (a) that six la a perfect Rubber (l.e., equal to the sum of Its aliquot parte), and (b) that, having divided one number by another, if you again multiply the divisor by the quotient the result is the original number; yet this manner of thinking is found all through the

times. Sertoii*a note (I, 610, 611) f Bede, “ ‘ “ -**

frevisa,s knowledge --- have translated "prisms" the L&tl& ^aoo&uyW#* ^ if he had been familiar with these____ y ;. :-,„v ' ' ...\ v t. - ■ - 14, A noabre feat hattc __ A word of explanation Multiplex end submit., being the dividend and For example, six may be the mmaor i submultiplex; six eontalM two, and

son with another, (Heath, II, 281). "A , — - in by nature first in thi division of Inequality pared with a grei ^ . a j*1QESfiLH fill it exactly.* • ■ " ■ • . .

' . ' . ... ' . r , . The number multiplex Buperpertlcularls contains it# aubmltlple more t .- . • ' : ' _" -. ' ' . S ” Z n Z S T S Z X?=“nto1'Ztmb=?™d1» Z ^aS-

line of dots), dot), end solidly“s (s S S ,LrS"Sr:K?r

sirs; c;:?:rz.:.:% 7 " UK) ' , ^ . r.awt *###%-

' . - ' '- \ I?. Tz .. *, nZ°oi J h ^ Z ^ l ^ t i l l t f 1-12^ ’"‘1U^ <1 10 M,i‘ h“ «• foUwll,e

rethoryque/ and wythcmt hit m y entlerly be knoven. Rhepfore It Is nuchoTao’t f f a l Juf °eSCJ0nCe3 1 not bo/ nd for ^ tob she^ott^ln the oyddlc o^h^ll^loncel^d^thare^holdeth

Anbu?°yr^8

18, Pletagoraa The life of P; at Croton In -51-

lamterlal In every way, essence, so should be created all stars, all sorts of revolutions. It

other but by itself, rtbn gives the foil its doctrine (I, 73): The early Pythagor and raised it to the rank of a

this days, led on the

SO, De Hensurls at Ponderibg. The article on ^Measures and

into more or learn of a system. There Is no mention, however, of jugera, actus, or other units of superficial measure.

' ' • : ' 21, Irmeional gretnesse. f -jt . irrational which have no exact exact value; nor, in em Steeles right to equal one, to the

step forward. The credited to Cassiodorlus by Cajori (1919, p. 6S).

Ami by art of tellyng and madires. Isidore (3.13.1) has this passage in sensible fora. The Inco fora of LB, TB, and FTdiJ leave two hypotheses: that the knowledge

^ oonco tiio and It went

24, Secundum. Haskins (p. ' " -i. enough to give forth

88, fry and liquid measure, and weight. The following note is free Knrplnskl The Romans employed dif: which, in altered form, cubic foot, termed an measure, and one-thin _ __ The conglus. of which eight make an of a gallon; the modjug is very nearly one peek. The systems of avoirdupois end Troy weights are directly french in

the French city of Troyes.

I have only found IV Heguia, xvltlB, and ic an follows: "hucach aedlflcaverat in teoplo: tenplun Ecaini propter regem Assyriorua." translates this as follows: "And the covert for had built in the hcuBc and the king's entry without. the house of the Lord for the king of Assyria." There is no other mention of this word, in either Latin or Greek dictionaries; Isidore has no mention of it; id! transmits it as *musa«$ LB has ”*iaae.« It seems possible that medieval scholarship tea cade an error here. • The following word, "corban," has the significance "dedicated to God," which clco dioagrees with the text.

34, Huge (also Huger) This man Is tentatively identified, in the absence of any positive clues, as Ugueeione do Regal; Paget Toynbee has this to say (in ^rt) of him: Ugueclone de Basel: of Pisa, grammarian of Cent, xll, author of a

in the Kiddle Ages, as la testified by the large number of MSS. still existing; it has never been printed, but the bulk of it is embodied In tho Catholloon (completed in 1286) of Giovanni da . Gonova. Ugueclone, w Bugultlo Pisanus, as ho was eommonly styled, was a native of Pisa; little Is known of his life beyond that he was born e. 1140, that he was profenaor of ecclesiastical juris­ prudence at Bologna c. 1178, and that he was Bishop of Ferrara from 1190 till his death in 1210. According to Vosaler

37, Macro Maercblus, Ambrosius Theodosius; Roman graamarlan and philosopher, flourished during the reigns of Honorlus and Arcadlus (3t6-423). The following note Is taken native eyatea of i wo op the gpelh < whenee we obtain the

*4, Twelf vneea makl# libra. Confusion lias arisen between - of a libra — both "unala.* foote (contains) sixteen are Insertions, understood In the text.) / X«v -54-

5 F*Hir twwA< I^ri# An hunPwt? 4 |Ni#fmr M ftpr fh—» m*$tf mrm m0 fi m >i Aaf (smr romffitu* aww fi (tm *»f fr j ^ fmom AW#AALm % & iS fW»^ — (>frr fturrAmf fwir AMnwAn CunAtf • ai«# of .vmoec# *nf fwrfctv miir Wiif • A# if fifrrr Af rr iwfi» & fionn# 6ef of eomk-ff Am# fa fern nomftf pe mypAM####MWk Vv I# OWMO AM# (#W ###C fC OKMf ntmilC ;: fruf is A f w A»#rf 6df # ft* A^e* msr 6f *fer#«imr ArH f (A#r*** #n#rf momAf of n^kr ,#(mf mAr nMdf 6f #tprff mtom#iKfkrf fin" • 4nwel»<**(*&#m#vofnt yAf oomt |Hrt iA m#» *# ff o*rr CmfR Atf m frc * nmurfWSAef CWow#wS|WAfASF ^r*< AM# fbKW AM# OffT AA / HnAtofFw K*r*r*+f*fir*9+T* rr rw*f nomki# IS m ftS <5m^ (#m oftleon F U i# Hfcffnf f IS pATtf# a«9 (am I# mifArH# fTo^Wn^ FifnWmt oon «d#pn ima4| tnonffot fet fAftS »#atm# m nm w nwwAorl a M at amoom WOOM IWIS onfim^WV il % ns#r fr r»CAftN*#rf#f fkwir*x#fwtr iSf\%o W fiytrMi Awff a ;■ i fiM#m#@F#wm# lit"' n««r AM# Coif frrof IS fmmo Aa# of niff An# Co/f f#f f**nr a»# ^aI> prr4f tAfcmu An# fiA^forof if Aon An#iS m#mi WfTWA^IFl^f ft^C An# fm4*ierttnf*r i# pf n#niC?< fOr AMfFAFTBin#Ari^ mAr fc f Mf# cuonr sKVmnf hv nf &# f^(AfrM8iyf,M w a W af^ h t A# IS ##Kr AM# MW iwor h as ftn ten Fount foont AFH iiW W F » » # f w s # # nc nsAtnf We am# f#rn n ptiftr fpfw amo no# m A fW M ^ F A f o ^ t AM# ff f i w n o * a# (wfir nonAfS (ht# y tntw A 1*0 «• AW A nonWC fir mtr MAMr #r f «4# fiSAft AM#CA^Frof.S#Ff M ###r AM#^ntA0M&6FfMK^ nWnAMy 6flWf flFW AiOlMnf AMS^fAf ffnmr wiMr F fMiFF ^ 6 mamA a r«Ap 6er oonLft oon fir inr tec Ct f^oFr Hm#f IS AM #Mt AAmtit fAf Mtf of mu/ 4 fume mtfwTnff fir FAT* f*A*rr 1M ^oArAMF ofoPAnomArS ASfimrf nWnrr ArpAMf msikroMAMtFf^"*^ ^ * " AnffWAr fAffirr o#Ar nAinAts #miA MAW&OS Com MAMA& OOnttA ftp Transcript of last ch,ajLter of ramiscrlpt.

Con to culs operls1, Capltulua CZLVI,

This t)Qt to hausi> schortllche y-pleuntcd hore of nccldentos of kyndo- llche plages as of coloures, saucmres and odoures, of welgtea, llquouree and aesurea, of voice and of aome, by ynov at >is tyme. Ffor aa I geese, to p& boystorise and to the eaale |>at be# yllche to m la gift, #llke binges of propretees of kyndellohe binges that be# digests end y-treted

In nynetene pareelles schal suffice to fynde aoa reaoun aM llkkenesse by what cause holy t|*ltte vaeth so redy llkenesae and figures of kynde

ende of #ls werk am I dede In the bygynnynge #at In all #at la In dyueree aatleres cooteyned In this werk right Xitel or lumght haue I sett* of some owne; but I haue sewed so#nesae and trou#e and y-sowed #e vordes, aenynge. and saves, and ccxaaentes of holy seyntes and of phllosopheres that the '" .' . ' - ' - i- sample, that may nought for endelee many hookas aeche and fynde all #e propretees of #lnges of #e (which#) holy vrltte aaklth aencloun and eynde, '' : ' !' - . <. :... . _ may here fynde s m dele what be deslreth. Itoat I haue y-take Is symple and ^ - , . .. - . ^.4 . _ y~"y" boystouse, bat I hold* #ey ben goode and profitable to ®% #at am boystoua, and to o#ere such* as I am. #erfore I rede #e symple that #ay despise aou3t #la symple wharaie #ey vnderstonde# #ls pleynellche and at #9 fulle.

' ------' . ' ^ - -Ly- . .. . and #at y-do and leue on here owne auyseaent and wltte. If #ey wol ameMe and correct* what Is InBufflclenllche y-aeyde and hem sem# wor#e to do more #erto, #at #ey do more #erto, as God 3lw* hen grace, #at what is by me rude and symple so® dale bygonne ray be by here wltte and grate

1% MS. not clear. ' - ■ ...... ilaedoae y-aade complete and perfyte to His worschlpe and bllsse Is

Alpha a n d w , bygynnynge and endyngc of alia good, that (Is) hlhe God and

glorlouoe, lyuyhge and reynynge, eueraore wl^outen ende. Arnsn.

, S a aserJyBt sL Us* SL sources given In aanuacript.8 ^ # Bndeles grace, bllsae and ^onhynge to dure Lord God, All Weldynge,

U s e trenslaclouns I ended* at Berkeley* the elxte day of Pfeuerey, the

sere of Cur Lords a thousands hre hundred, fours actors and «istens. The

and twenty. The seers of my lordea age, SlreThosae, Lord of Berkeley,

that mads ms make this translecloun, seuens and. fourty.

This* be$t )>® auetoura that be$> allegged In hies bokes. Augustinus.

Aasatlflus. Ambroalus. Haymo. Alqulnus. Anselmw. Basillus. Beds.

Bernardus Clprlanus. Eusiclus. Eusebius. Crlsostomus. Damaslus.

Dazmsoenua. Crlaorua. Dlonisiua. Elipltraa. Ffulgenclus. Grcgorus.

Qilbertua. JsrosGus. Isldorua. Imtocentiua. Leo. Papua. Mlchal

SootiUB* Nazarenus. Orlgenss. Orooius. Petrus. Senior. Panphllius.

Petrlslus. Fabanus. Robortus Lincolnnus. Ficus de Sancto Victor. Eycon

Comas. StephanuB. Stratus.

Inter phos sunt by auctores: Arlstotlls. Auloenna. Auorols.

Alga sal. Appoloaua. Alfredus Angllcus, toly medlcus. Aselepldes magus.

Boeclus. cttharo. Cato. Clplo Affrloams. Constantlms, medlcus.

Deaosceus. Dlascorldes. Democritus. Donatua Geroanlcus. Erachtuo.

Bpelus. Knelldes. Bgldlus medlcus. Ffiaologus. Gallenun, medlcus.

Xogathus. Caldeus. Ipartus. luuenalls. lohannlclus. Kallxtus, cus

slue athemesls. Lentlppus. Macroblus. Herecurlus. Mlselak. Astrologus.

Sclnus Delphlcus. Outdlus. Orbasius, medlcus. Paples. Plato. Plstearlus,

2. This section follows preceding text Immediately. / ..-r

. glmtom* vrmis. Pttioloeeus. Varro. Vlrglslus. Busuclo. ?isanuo. nilllana

: V - - i Isto ot allorlum aaltoma la latls Ubellla verba la dluersls loels

- . - .A

Explicit traetai d : ^ T ^

'...... /

: -- ' ' . r f "

X- - '' S.

..-trl.

TX ■ . ■ . X: . - -i'

? A Mot Latin Dlctlomry, et®. Hevlaed edltloa. Edited by B. A* Andrews,

revisM by Charlton f.

Book Co., 190?.

Ball, W* %. R. A ttteBC.' °L the Hl.BtorX oT Ics. 4th edition. London: Beemlllan, 1914. pp. 165. Bernal, J. D. vh» R^iai nr c«

pp. 488.

Cajorl, FIonian. A History of

Teem MaoedUan, 1919. pp. 616.

______. A History of Kathoaatlcs. 1st edition, 1896.

1986. 8 VOl.

Bnerson, °llver Farrar. A Middle English Reader. Revised edition. London:

Macmillan, 1938. pp. 478.

Haskins, Charles Homer. Studies in the History, of Mediaeval Science.

Harvard Unlv. Press, 1924. pp. 411.

Heath, Sir Thomas L., editor. The Thirteen Books of Fuclld*s Elements.

2nd edition. Cambridge Unlv. Press, 1926. 3 vol.

Hopper, Vincent Foster.

English and Comparative Literature, Bo. 132. Columbia Unlv. Press,

1938. pp. 241.

Isldorl Hlspalensls Eplscopl EtynologlsrvD Siva- -Cslglnvau Edited by u. ju

Lindsay. Oxford Unlv. ^rero, 1911. 2 vol. Sarton, George L. Introduction to the History of Science. Rashlngton: Carnegie institute of 1931. 2 vol. Edith, David Eugene. % theca t ies. Hetr York: Ginn, 1923. 2 vol.

^ I'" Rob

WJ VUluUti A#

Bradley, and others. Oxford Univ. Press, 1933.

Thirteen Centuries of our Bra, tier York: Baealllan, 1923. 2 vol Toynbee, Paget. Concise

.. . , • : . • . % ■ ' :

Vossler, Karl. Mlaevpl, Culture: AD. jntrpduptlon to Jgpnto. and %s Slices.

Hew York: Harccurt,. 1929. 8 vol.

; .. . - r : ' '

t; ■ v . .. :

vf - .

- .. - " ' " ^ '

% ja: "":w i -

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" a*.

/ .- .T .' - it, - GLOSSARY abouo, propj exceeding, above. acceptabaluD, sb; (L) originally a vessel for vinegar (L. acitabulun); a cup-shapad vessel; as a li

aconpte, v; (P) to reckon, estiaate, value, hold (a thing) to be so.

acorde, sb; (L) ha raony; in sausic, agreenenfc or harr,ionious correspondence of things or their properties, esp. of sounds. •

acountes, sb; counting, reckoning, or computation.

actus, sb; (L) (a) road between fields, passage for cattle; (b) a measure of area;;a. minimus, 120* x 4«; a. quadratus, 120« x 120*; a. ducUcatus, 240* x 120*.

again, adv; again, back into a former position or sta te ,

agentward, adv; opposite, against-wico. \UJ a

, ®b| (L) ambitus, eb; (L) space surrounding house, .. epace.

amphora, sb; (L) as a vessel, a two-handled jar or vase; as a measure, among the Romans equal to 6 gal. ? pts.

ampulla, sb; (L) a flask, bottle, jar, pot, made of glass or leather; a.snail vessel for holding liquids, furnished with 2 handles and swelling in the

angle, v; y-a nglcd, joined in an angle, placed at an angle,

angulus, sb; (L) angle, comor.

anon, adv; forthwith, at once, straightway; in the same course or direction.

aaooa, sco anon. anoynta, vj to B»ear or rub over with o il or unguent, an sis, sbj (L) handle. apyrous, vj to tsot; to pronounce fit, good. archa, sbj (L) casket, strong box. ' " ' ' - ' ' ' arewe, sbj arro*« arcwe, advj a-row, in line, in succession.' are metrik, obj (£,) tho science of arithmetic; also used loosely to include gedmotry. artaba, sbj Hgyj)tian dry neasure equal to 5 2/5 Boaaa o o d ii. ' artiOttlua, a; (L) of number, the multiples of ten. assay©, v; (F) to judge the nature, excellence, fitness. asccnbyngs, ppl, a; condirrant, approving, proper, fit, meet, according. aasls, ab) plur. form of Latin as; in general, unity, a unit, as a ataida-d for different coins, weights, measures, etc.; as a weight, equal to calculus; also the perfect number, fundanental number. According to the duodecimal system it is-divided into la parts, or uncias, with sextans being l/G, cmadrjis 1/4, triens 1/b, otc.; (For fuller particulars see Harper*s Latin Dictionary.) atsynno, adv; in two or aaro parts. awayta, abj in wait, in ambush; used with lio, lurk, etc. axen, eb# plural form of axe; ashes.

B bachi, sbj. (L. bachia) a kind of drinking vessel, a goblet, bowl.

bacyn, ab; basin. '

barel, sbj barrel, wine-jar, jug.

basket, eb; basket, woven-rced vessel.,

batus, ab; Hebrew liquid muasuro equal to 6 1/2 gallons.

benchiage, sbj provision or range of benches or seats at side of road. boncfeto, sbj largesse, favors distributed among tho people.

■ , ' ■ ' • . . b ic lip , r; to embrace, enfold. biholdo, v; to consider (witii mind), regard.

bimriua, sb| (L) branching, fork in tho road, binarius, sb> (L) dua lit y j a couple, pair, bitoknc, bj signify, mean, denote, express in xonls; bitwene, prop; in an iiitercediato position. bloT.'e, v; to in fla te .

, ' ' ' - v .-a- ' . blo^ynge, ppl. »b; spouting, blowing; to blow' forun iron balov/. boket, sb; bucltet. • bolle, sb; bowl. ■ boll®, sb; (L) bubble, boi'do, sb; board, peice o f wood, bote, sb; boat; hotel, sb; bottle, bound®, sb* lim it. boxtre(o), sb; genus buxua of small evergreen trees or shrubs; boyl®, v; to boil, brede, sb; breadth. brerda, sb; the topmost surf act or odgo; rim, brim, brink,

brood, a ; broad.

b r o til, a ; lia b le to bre--k, fr a g ile , b r ittle ,

bulla, sb; (L) a bubble.

by cause; because. . . e cacsabus, ab; (L) a cooking pot* . cadus, sbj (L) a large wine v e sse l, barrel, jug; as a measure, equal to 3 vm a, 12 congii. calathus, sbj (L) basket of splintss, -Bicker basket, calculus, sbj (L) a small weight, equal to 2 grains of chickpea, ealculjmge, ppl* sbj (L) calculating, reckoning. ca lix , sbj (L) ch alice, goblotj the measure of liq u id contained therein. caliis, sbj (L) Stony, uneven footpath; a mountain path, esp. path made by goats. calo, sbj (L) a piece or billet of wood.

Campania; province in Italy in %hich is located tho city of Hole, canes, sbj (pi*) basket woven from roodsj bread, fruit, flower basket, eariage, sbj a means of conveyance.

c&thinua, sbj (L) vessel for meat or drinkj a senring vessel or cooking pot.

caudron, sbj caldron, cooking pot.

celata, sb; (L) (pi.) an engraved vasej one with raised designs on it, centenaria*, sbj (L) one hundred of something,

emsour, sbj (L) a censor. Incense burner,

centuria, sbj (L) 200 jugersj measure of area.

csrels, sbj circlej continuous lino in one plane, all points of which arc equally distant from a point in that plane. cerusa, sbj (L) cerusoj white lead.

cease, vj (F or L) to cease, stop, come to an end.

eharg, sbj (F) load, turden, .... chilindrus, sbj (L) cylinder,

chirche, sbj church.

chorus, sbj (L> Hob. cor) a measure of 30 modii.

dates, sbj (L) vrieght equal to 10 dragms; a small measure, ladle for dip­ ping wine out of bowl. eiabra, eb$ this is probably an errorj it is uncertain what word should bo hero. ' ■ ' ' circu laris, a; (L) circular, round; a c. number i s a number whose powers ..****70 tonainate in the number itself. circunducta, ab; (L) a going about; a circle. cista, sb; (L) a woven basket, wicker work-basket or box used for keeping money, clothes, books, fruits, eietreUa, sb; (I.) » small cista ; chest or box. ci^s, see. sipes. _ . . - „ . clone, a; clear of obstructions; doan. clepe, v; to call. elore, a; transparent, or perhaps either transparent or translucent. clima, clyma, sb; (L) «a land measure of 60 sq. fee t." H L D. A measure of 60 x 60 foot, laid. 15.15.4. clos, a; enclosed or shut in; shut up, confined. ooaceruacioun, sb; (L. coacervatio, -onis), a heaping up, accumulation, heaping together. oodea^iua, sb; (L) a spoon with a point at one end used to pick sn a ils (cocleae) or shellfish out of their shells, hence the name; a measure for liquids, esp. in medicine; a spoonful; 1/2 cheae; 1/144 cotyla. cootila, ab; (L) a measure, 1 1/2 dragme.. eomo., sb; a measure. 100 dragma; the Greek mina (see footnote). co»or, sb; (Heb.) honor, homer. coeparisoun, sb; comparison; the finding of likenesses and diversityi,, ccepita, sb; (L) junction of ways, junction. composioioun, sb; a whole, a unity, a cmpleto homogeneous unit; consti­ tution, consistencies. coepositus, sb; (L) composite in structure, not simple; a c. number is made up of the articulate and the digit — as 11, 12, 25, 24, etc. ooBpot, sb; reckoning, computation. ooepomwd, ppl. a; formed, compounded, made; a number i s compound when i t has a common sutrrultiple with a mother. comprehend, vj to include, comprise, conyn, aj comon, fam iliar; public. coayns, sb; used in the plur. as a lower classes. comynte, sb; the body of conceyuynge, ppl. sb; power of conceiving, gendering, conoourc, sb; meeting, conjunction. eoweuplfteibill, a; cf. iraseibill; that part of the soul in which the appetites are found. conduyt, sb; artificial other liquids. confort, sb; comfort.

as corn or nine, later used to include money. eoagtas, sb; (L) a liquid measure equal to l/C Roman amphora, 6 or 7 English pints; a weight equal to 12 pounds. conlunceiouB, sb; conoun, sb; (L. ?) consonancy, sb; eoBCord. conteyne, v; to contain; possess, hold; contrary, a; opposite in position; opposed. contrary, sb; 1 oophimts, sb; (L) a >r d ir t. oorbas, sb; (L) a (to contain offerings of priests); * basket, a small basket; a corporal, a; bodily; corptiMmt, a; m 1 ■i corrupt©, a# sour, ' . coatrel, sbj a large bottle or a raall keg. cotula,sb; (L) cotyl:v; a snail vosselj as a measure, equal to an hsaina (emina) or half a sextarius. eouplynge, ppl. sbg joining. cribbe, sb? a wicker basket or pannier. oribniB, sb; (L) a source, sieve, riddle. eris-tal, sb; aryetal; glass. erokke, sb; olla, crock, jug. culms, sb; (L) a cube. ourrii'orum,' a; word doubtful; evidently "having holes, uievo-lia-hv custuee, sb; king's duties, customary taxes, cuype, sbj a basket, plaited basket or hamper. eylieoa, sb; scribal error for cilioncn, the connicn nans for caelata.

. : ■ ' D -■ ' : _ ‘bsas, vj (5 sg .)« L do, daro - to give?) word doubtful, defeuto, sb$ (F) uant, lack, absence of ecmething.

degre, sb; second place.

de, sb; part. ■ :

dele, v; divide, part; measure.

delyage, ppl. sb; division.

deaario, sb; (L) tonneso; the nuaber ten.

denarius, sb; (L) (The 0 E D and tbo 11 L D give this as a.weight equal to or nearly equal to the Greek tirugnu. Accoitiing to tula Md. this is m error (which probably arose through the existence of two scrupuli); & . weight equal to ten Biliquis or pano of silver.

depart©, v; to divide into parts.

depnee, so; deepness, depth. —67—

4mlyw«i,*)uay ab| dosign&tioa; indication of seas things b/ ono thing, designs, v; to fm te «iccpixilag to design} to .lay out, plun, nuke. dot^-yr.,, v; to act forth. diapasoua, sbj (L) in nusic, the interval of an octavo. diapento, sbj (L) in kusIc, the interval of ono fifth. : : ; . . ... •...... dlittegrason, ob$ & geometrical figure the exact shape of whidt ius not been identified; Isidore (b.11.2) at'sxatheton grameon; L S ui&crato congrejaon. dtlateeseroun, sb; (L) in music, the interval of ono fourth. digitus, sb; a digit; a rerrhor beneath ten. dijpd.te, sb; quality o f being worthy; worthiness, excellen ce. dinimt.-if, a; in nusiber tiieoiy, a muber Kh;>oe parts when added total less than the nunbar itse lf. disimtus, ppJU a; disdniuhed, ssall, clisimtivc. diadt, sb; dish. discrete, a; tbs opposite of continuous. discu^bonto, ,b,

diuercun, ppl. ob; (L) lit. «. turned different nays «; a branching of the wtys. ' ' . diucHiculun, sb; (L) a wayside stopping place,; diuinite, sb; divinity. dritta, sbf dirt, druye, aj dry. duoila, sbj (L) a •Rcighfc e^ual to 2 sextules, l/o vncia, l/56 asaic.- dxirc, v; to endure; to contiime. dwryng, p p l, a; lasting, enduring, continuing in existence, dy-j for xrords beginning r.ith dy- see also di-. djfmumiam, sb; measurement o f extent, dyuers, a; diverse.

E effectualliche, adv; as the effect of a causo. eft, a; near, convenient; adjoining. e f t , adv; again, la te r . e ig te , ab; eigh t. oi^er, a; each,

electuaries, sb; (L) a medicinal conserve or paste, consisting of a powder or other ingredient nixed with honey, preserve, or syrup.

element, ab; basic idea; a r e la tiv e ly simple substance of which a com­ plex substance i s composed.

eiaicadiiae, sb; (L) heaicadiua; a vessel equal to 1/2 cadus.

pound.

eelatia, sb; (L. amystis) the emptying of a cup a t one draught,

ende, sb; lim it, board; limit of extent, at origin or termination,

ondeles; sb; infinity.

enoforw, sb; wine vessel; Isid, (20.6.1) ocnopborum.

ensample, sb; exeusple. #*&i, eb> (Hen.) a neasm-o, used for gr?Ln, ndl, etc.; an cpioh. oscas, sfcj (L. gen. sg.) food; oachetour, ab| (Ep) govearcacnt tax collector. esasneia, obj (L) bade constituent substance (tangible or intaa^LlxLw)* esycncliOllche, edv? in essence, cscentiaUyj in basic nubataaca.

.euelonge, a; elongated; having one-axis-tevs^er than aastharj oblv»>g. , eueee, a; of am angle, eons 1 to 90°. eueoa, adv; in equal parts, ovonly. euericb, prom; each* euorich, a; each. euydent, a; plain, obvious, apparent, evident,

F fablis, sbj (pi.) foMme. fore, tj to iuppen, turn out. factnsase, ebj compactness, density, solidity. fayle, Vj to fa il, have -lack, be deficient. feotu, sbj supports; feet. felyng, ppl. sb; susceptibility to the higher arid core refined emotions; emotion, feeling. fe r , adv; far, yfere, ad?; together, in corip-my. femes, hb; extent, distance. for{)2 , sh; fourth, fests, sb; foast, banquet, feyno, V; to icigu, represent. ' fig, sb; fig. figure, abj representation, likeness, shaje. .

filia, abj (Sr.) faolosj glass, filitm , sb; (L) a tliread, string, fiola, sbj (L) phi;0.; small glass bottle. fiscella, sbj (L) a roran basket the bottom of which is scaled with pitch. flseua, sb$ (L) a Back, bagj a state treasury, privy purse. fletyngo, ppl. a; flowing, liquid; unstable. flyringo, ppl. sbj showing up; brightening, polishing. fondynge, ppl. sb; striving, yearning toward. fongo, r; to embrace, include; receive, take, accept. footo, sb; as a measure, equal to 16 inches according to MS. but see note, fore, sb; track, furrow, forms, sb; fora; used to denote angola on p. 29 in the description of tho creations of God on the first day; in scholastic philosophy, tho essential determinant principle of a thing, that which makes anything (matter) a determinate species or kind of being. foiov/, sbj furrow, rut; mark made in passing. foulo, sb; fowls in general, flying things. frayel, sb; basket for packing figs, raisins; rush basket. fol, adv; used simply as an intonsificr; completely, very, exceedingly.

G gaderynge, ppl. sb; gathering. gauta, sb; (L.< gutta, drop) a narror-nockod vessel, cruot, flask, from which liq uids were poured by drops.

gasofilnciun, sb; (Gr.) treasure chest; a treasury.

gcmctrl, sb; geometry; tho science o f the measurement of lin o s and areas.

gandro, sb; kind. v--'-

gcndra, v; to originate?, begot, generate, geueracieun, sbj generation, the fact of being begotten; the whole body of individuals bora about tho sane period, gonor, sbj (1) through a confusion of the initia 1 sounds, goaor is used to

534,4 liter according to the Jewish Encyclopediaj (2) the gonor itself is apparently a measure of approx, 5.1 pin ts.

Grev/, groo, gru, grn, sbj Greek, people or language. grots, sbj ancestors, el4ars» grots, a j great, large, grayno, sbj grain.

• 1 haluendol, sbj half, the half-part, hattc, pplj called, named, hight. he, prnj he; also they, heed, sbj head, suurce*

hihe, a; high; fa. road, the public road upon to all passengers, his, pm; his; its. hisoplexoa, so; isculcuros, or equal-sided figure; equilateral. The shape of the figure is not aide clear. hole, a ; whole. holow, holowg, a; hollow. boofel, »b; that by which a thing is hung; hinglc,. or hinge, to o l, a; whole.

(y-)hove, ppl; lifted, raised; pulled, hucche, sb; a chest or coffer, in which things are stored.

(y-)huddo, ppl.; hidden.

Huge, Huger, sb; ■; Uguciona; seo no to . -’r

hulke, sbj th-.i cleaned carcass; the hull or husk. b u lle, Mb} M U . . . huole, cb; (LB Isid. have «3iliqua«) as a coin is l/id4 solidus, as a weight equals 1/6 acrupuius. The eord has not been found outside of this MS. tuple, sb; heap, pilo, mound; a little heap. taplfng, sb; a little heap, a heaping.

I iispar, a ; odd.

ioyaed, joined.

two parts of the passion were held to arise; and which was superior to — part in which resided the appetites.# (0 I §)• irracion.il , a; of nuabera, parts. isc o , sb; (L) meaning nut found. ite r , sb; (L) way, road, path; a going, a journey.

Iu«ensa, mb; (L) -measure of area equal to two actus; lugorum actun i s a measure of area 240 f t . x 120 f t . *

■ K keruyngs, ppl. earring, dealing; cutting.

knygtonc, a; knights*, military; this fora is genativo pi.; k, vay - military road, tha high way, which was protected ty the Eing*s peace,

kyndeliche, ddv; according to their disposition; appropriately, naturally.

L labium,_ sb; (L) lip ; edge, brim; basin, tub, bathtub,

lagena, sb; wine vessel, little barrel,

laguncula, cb; kind of lagena.

lame, lances, sb; (L) plate, platter; balance pan. laseo, .aj loss* lauatoriua, sbj vossel for naeMngj tub, bath.

Icbarata, sbj (L. lebss, lobotis).a copper basin, kettle, cauldron, for cooking. / lebs.-i, ab) (L) seo lybarata. led©, ▼) to cai-ry, convey. loede, sbj lead*. • lej^Lr, cb| leather* leuci, so; (L. leuga) le .gue) 1000 paces, lib ra, ab) (L) pound; 12 oa. likyngo, sbj likonesaj in the usage on page 5 it seens a scribal error, the L. version having ”votiua!i - having to do with a vow; it nay bo > eoae fora coming from l,lig e n which has the caeo rout iseuiing as rotiu a.

' -- / ' ^ liqueure, sb; liquid. lombw, sb; (L) purse; a general sense of pocket; coffer with coapartaenta.

Lucauns, sb; abbrev. for Lucretiuo*

Inoerna, sb; lamp, lantern.

IncisBis, sb; (L) a candle. ludoro, sb; (L) lavor, or basin in which ritual Bashing was dona.

lyne, sb; an extension without breadth between two points; a nathesatical

lyno, adv; in lin o .

a; of a nunbor, one which zany bo represented by duts in lin e; as, for instance, 5 (...) or four (....)

X

*&cro, sb; abbrev. for Macrobus. .

manor,' C5 kind o f.

Mortar, sb; abbrev. for Martianus Gapalla

aatiero, sb; substance; in the quot. from Genesis (page k9) it refers to formless matter, which the L. version spouko of as "nateriem infonnen". (y-)acdlid^ ppl»; aised, singled. ceno, Tj to tend toward, seek. more, soj lim it, boundary; lim iting point. motes, sbj (pi-.) foods in general. mtifcti, v; to moas-oro, determine the dimensions of. cietrota, sbj (L) (Or) a measure of about 9 g a ls.; an Athenian measure, equal to 12 congii; by transferrence, a tun, cask, jar. might, sb; a jot, chit, infiaitecmally small (Immaterial) portion; might, power. a iliia r ia , sb; the Roman m ile; tho original meaning was m ilestone. sioder, sb; source, cause; mother. sore, ab; see mors. .. modiua, sb; (L) the Homan com measure; peck; "16 sextarii" (H I# D) aoola, sb; (L) according to Barth., a large boxl; in classical L. a millstone or a type of grain. momentum statore; (L) literally, "the movenmt of tha scales,n “tho move­ ment by tho steelyard .« Barth. moot, v; must, bo c-apallod to. sore, sb; origin, source, root. more, a; greater. mors opium, maroupim, sb; (L) bag, pouch, mulgiariua, ab; (L) milking p a il. multiplex, sb; & number wnich, considered in comparison with another mmbor, contains tho less number an even number of times; a multiple. M = ^ ^ . multiplex supcrp-urticularis, sb; a number which, considered in comparison' with another number, contains tlie less number core than once with a remainder of more than one. S Z x(s) plus (1 plus y).

iimltiulicacicun, sb; process of a; the result of process of n. fliusa, sb; (L) box to keep the offerings of kings? see notu.

•myle, sb; the Roman mile, equal to 1000 paces, 50C-0 feet, 8 atadial fields; . H L D suyo it has been estimated at 1618 English yards (485-1 feat). .

nysclepe, tj m iecall, aisnamc.;

H nede, vj rnuat, be compolled to; be necessary, nodeful, a; useful; requisite, needed. noidti, y; to near, c o k © noaxv ^ t nerre, adv; coup, degree; no-xor. nola, eb; (L) b e ll.

BorlsohyBge, pple ob; nourishing. noujjor;-pm., another; a, another; conj., neither. nomsiisma, eb; (L) piece of money. ny5e, adr; near, high. ' , ' f , , . — —

0 obliquua, a; (L) o f an eagle, one rhicii i s le s s than 1G0° and noro than 0° but is not a right angle. obolun, sb; (L) a weight equal to 5 huoles or siliquiis, 4 calculus. obtusuo, a; .(L) of an;.angle, more than 90°. odde, a; of musbars, not even. • of, $«r@p; of; from. of to, adv; often, rcore tlum once. olla, sb; (L) jug, crock; cooking pot. eon, sb; one, u n it, oon, v; to join, bind, made one; to join, become one, unite, oonliedo, sb; oneness, unity of existence. oppose, v; to challenge, confront with objections or hard questions; poso; examine, interrogate. orbita, sb; (L) wheel track. ordoigae, tj to setup, establish.

Orion, sb; ths god. ortogonium, aj right-angled, rectangular, orthogonal} as used here it saeas to scan a right triangle. ^ t : ^ ,, . , oughna} intensiT ier, own. \ , . ': "' . " :: oxifalxis, Qb| (L. oxybaphus) a neasuro equal,to acetahulua, 15 dragaa} .according to K L D, a vinegar cup.

P panor, obj a basket. pas, sb| (L ?) nooning not found. panycr, sb} eeo panor. peurapsis, sb) (L) a large square dish for the dessert, a dessert dish, perfit, a}:soo perfite. parisch, sbf & c lip , young tree, esp ecially a young uiliow tree. parted, ppl. a; divided into parts} divisible into parts. (Tlie L. word pariter, of wMch this is the translation, has the sense of equality of parts. parties., mb* (L) a measuring rod; a perch,

particulere, a; particular} possessing separate entity.

P«rtye, mb; a part; of a number, one of the aliquot parts,

pace, sb; a pace, equal to 5 feet.

passe, v; to pass, exceed; to pertain to, care for, concern, reck of.

p atella, sb; (l») a pan.

patana, oh; ( l) a shallow dish, plate, shell}" perhaps this cay mean hero the shallow dish or p late, usually circular and of silv e r , on wliich tko bread is laid afr the celebration of the Eucharist,

patently, seo dispansis.

patera, mb; (L) a broad flat dish; a libation bowl or saucer,

pbluis, sb; (L) a basin, lasrrr. -7T.

perchs, sbj a 65 foot; a length is xu.a loot. perchemyn, sbj

particular. perfite, vj to become perfect, come to perfection.

$wr»cda, see p-irisch, pcrcho. pesible, aj able to bear hardens, peisable.

'P&dlatcrias, sbj (L) philacbery, pliilologia, sbj the allegorical history of the culture of his times written by Martiama Capelin (see notes) "Do Kuptiis Piiilologiae et Uercurii’1. pleche, vj to pitch, stick with pitch. pier®, #J peer, equal. " '

pireno, sbj a sharply pointed shape. pUuOs, ,(L). tto sooaotrical figuro, a pgnsudd.

p ix ie, sbj (L) box.

plaaeteB, sb j (pi.) plants; young trees, slips (laid, plantaria).

plays®, pleyno; a; plane, existing in ouo piano only; in plcyna foot, on level ground (>L. in piano podo).

yl& ym , sb j a plane superficies.

pneuma, sbj (pi.) things having to do with air, as sounds. (L. pnAaticus, having to do with air).

pocoltai, mb; (L) drinking vessel, cup, goblet, beaker,

pondoribg, sbj Do Pondcribs, (L) concerning weights,

poor®, ebj pores, openings, holes in surface,

ponder, mb; powdar.

poynt, sb j in gccnotry, that which has position but no dimensions,

prenie, sb j print, impression. element; V? d W has "pxynced," from the verb "prink" which has to do with setting up in a high place. . r- _ preeento, v; show forth, represent. processc, sb; discourse, discussion; to make p., to set forth, to tell of; to organize. procecsioun, sb; the act of coming from. pteposid, ppl; set forth, constructed; put forth for discussion.

$ qmdrans, sb; (L) a fourth part, one fourth; of a coin, one fourth as (aesiu) or 3 xrncia; of a weight, one fourth pound or 5 cythia; the L c ic lu s. quadrate, a; square. qualite, sb; property. ? quatrable, a; four tines as great; a quantity or number which is four ticos as great. • ■- I-.-. sb; (L) tiiat which contains fiv e ; a weight equal to 5 sextu rii or 10 pounds. quisquilariuu, sb; (L) a container for quisquilius material; a container for just about any rubbish.

rape, sb; selves. raptorium, sb; (L) a vessel in ' rectus, a; (L) of on to 00° or perpendicular. redact, ppl; brought together into reduct, ppl; compressed in # rtire, vj to erectj to fora, create, build up. resoun, ebj account or explanation; ratio, relationship (of the circle, eatons i t s p arts)...... , ' rests, sb; an abiding position. revyngo, ppl; lessening, taking away. , , itrole, ab| source, origin.

*y»de, sb; the bark of a tree or plant.

; S ' a adds, adv; solidly, densely, compactly; massively, heavily, nalere, sb; a salt cellar, salinun, sb; (L) a salt collar;1 earcione, sb; cultivated lands; lands for sowing seeds, sartago, sb; (L) frying pan, baking. satosi, »b; (L) a Hebrew measure, equal to 1 2/2 nudius. shodo, v; to shed; to spill; to part coupon/ with, seheld, sb; shield.

(y-)ohcmt, ppl; put to shame and:confusion; ‘ Injured.

•oiwwed, >pl; showed, demonstrated, schore, a; thin, dilute, eehlre, soo schore.

science aatlissiatica; tho mathematical sciences, including arithsetic, geometry, music, astronomy.

science of nonbrea; arithm etic.

sciphus, sb; (L) a cup, goblet.

scriniw i, sb; (L) a small box for money or valuables.

sorupultts, mb; (L) the L. denarius; as an apothecary*s reiglit, equal to the dragma; one twenty-fourth of an uncia, a scruple; also noted in MS. as being equal to both o huoles and 10 huoles.

143904 scutella, sbf (L) a dish, platter* --.f Sscundus; a philosopher — Tpotisj see note. soldo, adv| the use here is uncertain; "passing* nay/bo understood, or the usage may be idiomatically correct as it stands and moan something like "few occasioa#"* sezaisGis, sb; (L) semi- or half-aasis; as, assis %as the unit of weight, - although it has beon replaced by the uncin at tho time of Isidore; one half as, one half uncia. semita, sb; (L) tho path of non, opposed to the high way. somiuncia, sb; (L) one h alf uncia, sta ter.

Senior; beyond tho fact that s Tabula chsrolce.. no other referred to sens, sb; shortened form of HE enceus; incense, scent. sense, v; to scent with incense. sebe, v; to boil, atos; to soak, steep.

. '■ eette; v; to pat to, add to; to give, present. e « ta r iu 6 , sb; (Q a weight equal to 2 pounds; as a measure, equal to ono sixth congius,- V .■ • ■ ' : ' ' ■ : sextula, sb; (L) solidus; r 1/6 uncia.

•ie lu s , c iclu s, eb; (L) one fourth uncia, ono half stater; two drags.as; in

holy. writto it equals an uncia, but commonly it equals one fourth uncia. algne, sb; figure or image; statue or e ffig y .

■iliqm, sb; (L) MS. notes this equal to one twentieth of tho solidus; in classical L. equal to one twenty-fourth solidus; a very small weight or measure; the seed of tho carob plant. simple, systple, a; of a number, prime; in general, pure, unified, homo­ geneous, of a nature which is unalloyed. sizapliciter, sb; the essential unity; one-ness, simplicity.

singular, -sr, a; denoting ono person or thing, not plural (banco not divisible); outstanding, unusual; sole, alono, only one.

siphon, sb; (L) fire bucket; evidently seme sort of leather bag with spout or hoso on i t . • alfree, ab$ (pi.) timas. i lt e la , sbj (L) bucket} a bucket for drawing vrator.

ob} skill, ingenuity. slidei> a; slippery, unstable, sliliche, advj slyly, secretly. sfjeJjo, aj smooth, fros fren roughness, aoeoura, sb; suecor, aid.

(y-) socle, ppl} soo seJ>o, sole, a;;sole; alone; singular. solidu s, ab; in geometry, a solid or three dimensional body; as a weight, a gold coin equal approx.- to 25 denarii; of a number, one rliich i s composed :-f the product of throe numbers. solidus, a;-the geometrical and numerical meanings of the adjective follow the substantive meanings. s o b , pm; any, aiQrone, one. so«# some, cerno, a; cone; a certain ono, unspecified, of (something). Sorter;, so; Socrates, sotil, a; delicate, fragile. sowno, sb; sound, to tie. sov.'ne, v; to sound, rin g, naira noise. spedaful, a; profitable, advantageous; helpful, spore, abj sphere, region; in geometry, a solid spherical body or ball.

Spire, v; to breed, bring forth; to inspire; to breathe forth.

•pissitudo, sb; (L) thickness. (>L. apissus, tiiick). splynfcra, nbj a splinter, splint; a long thin strip (of cane in ),

cuype, sb; no d efin ite meaning i s found for th is or analogous ferns; . according to the US. it is eporta, a basket, plaited basket or h;imper. gpousaile, sbj a betlirotbxl.,

8qu,ro, aj it is possible th-.b till w . * that all its angles are,right anglesj it is possible also"that'it means simply having .four sides more probable*

atodlol feld, 8b; a field mtadixm, sb; (L) one eighth o f a

st,.ter, sb; (L) a weight equal t<

etatere, ebj (l) & steelyard; a

stoic, sb; form (?); place,

etedeiaet, a; unchanging, regular* a X. stent®, ppl; see slynte.

stondyng, -jpl; this i s possibly, a scribal for understanding; than that I have no information noz itly what i t •toon, sb; stone*

stra ta , sb; (L) str ee t, \:ajr.

strei^ ht, str ei^ t, a; narrow; confining; straigh t,

stymie, r; to oeaae, step*

styntyngs, ppl; that ceases, has coasod, stopped.

sublecte, sb; the .Aristotelian nsubject of attributes"; the quality om which attributes occui'; quality.

submultiplex, sb; & number which, considered in comparison with another number, is contained an even number of times in tiio greater number; sub-mil tipis. (S = xc).

8utoau].ti>)lex superparciGns, sb; a number wliich, considered in comparison with anotlier number, is contained in the greater .nuaber core than oi with a remainder of noro than ons. K - x(s) plus (1 plus y).

subsuperparcieno, sb; a number which, considered in comparison with ano number, is contained in the greater number once with a remainder of than one. (S - s plus (l plus x)).

subsuperparticularls, sb; a number vsliich, considered in comparison with iinother number, is contained in the greater number once with a resu. of one, S - s plus 1. superparciens, sbj a nuaber vhich, considered in comparison with another number, contains the less number once with a remainder of more than one. S — s plus (1 plus x). superpartictularis, sbj a number which, considered in comparison with an­ other number, contains the less number once with a remainder of one. 3 -3 plus 1. superficial, a; having area or su-erficies; of a number, a plane number, or one which may ba represented by dots arranged in piano figures; three, for example, may be represented thus: and four thus: :: * superficies, sb; area, plane surface, or two dimensional surface; an area with no thickness. superfluite, superfluyte, sb; excess, superabundance. superfluus, a; in numbor theory, a number whoso parts, when added, make a greater number than the number itse lf.

«0» p le , a; see simple.

T tale, sbj reckoning. talentum, sb; (L) a weight, the largest used during Honan and medieval tim es, whicli c<£ualled variously 50, 7k, and IkO pounds.

telum, Sb; (L) (pi*) weapons; la id , & L 3 use ferrenenti here, or instru­ ments of iron. - -

teritories, mb; (pi.) lands lying around towns.

tenayno, v; to lim it, bound. ,

thamaristus, sb; the tamarist or tamarack tree. (>L tam oriscus).

Jjere, edv; where; tiiere.

i>erto, adv; lik e that, in that way.

Jxiues, sb; (p i.) tMwnea.

bridae, a; the third; the ordinal number three,

hries, adv; thrice,, throe times.

iarittene, sbj the cardinal number thirtoeu. i>ritty, sbj tho cardinal number thirty. thwytynge, ppl. sb? cutting donn, whittling, paring, shaving; shaping by paring. The barrel staves were evidently shaped with a draw knife or sone instrunont of tho sort. hynne, a; thin; of slight density.

; : : M iles, sbj (pi.) a common abbreviation for len tils. tintinabulim , sb; (L) a b e ll. , » todele, v; to divide, separate. tokne, sb; nark, token, sign, tokne, v; to be a sign of, denote, represent. tonne, sb; (L ?) a tun, large cask, barrel.

Maeitee, sb; (L) (pi.) crossways, side ways, bypaths. (L sg. tranis); trade, v; to tread; to press upon by stepping. tre*i88iB,■ sb; (L) & weight equal to one third solidus. t r is ilio , sb; (L) that which has three feet; a v e sse l which has three fe e t. trutina, sb; (L) scales, balance.

Trunagestus; the follow ing note i s taken from Hopper, p. 55; The mythical author, Hermes TrismeMstus, is generally identified, with the god Thoth, whose name was used to give authority to the profundities of a group of Alexandrian scholars. ...the astrology accounts for tho superstitious veneration paid to the thrice-great Hermes by centuries of alchemists arid other workers in eagle. tweyne, sb; two; a pair, a couple. tweyne, a; two.

V v m m , sb; an instrument for winnowing grain; a basket of special for* used to separate grain from chaff. ventil&brun, sb; (L) see vanne. vergis, sb; (pi.) (L< verge, to bend) "bending things?, bendable things"; withes?. '• verray,-a; true; iropvriy> fitly. -

Y!iJ3ti^iu£:, cb; (L) print o f foot; track, viols., eh; v io l or phial; a vosbc! of snail or sodsruva else used for holding liquids. vzicho, sb; (L) inch; r. measure of length approximately o .uol to i t s present value** • vneia, vncsni, unous,* vace, eb; one tvrolf th; as a ftelghL, 1/12 of libra; as a laansurs of area, 1/12 jugera* vaoriyautlidte, adv; irregularly, not in any regular order. vni'crtol, a; of a casber, an odd number (or cue which c.mnot bo divided evenly)• vrceolus, sbj (L) a asall pitcher; the diminutive of urccus# vrm, #b; (L) a vassel, properly used for usher, of the dead but applied to other uses also; as a measure culled qu-irbcriim. (This is per­ haps the origin of the quart, for a funeral urn holds about one quart). vterf sb; (L) a bottle of leath er, a leather bag.

■ veil, sb; veil, origin, point of ahich scuethingc springs, r/one, v; to «ecu, think, expect. vexo, v; to wax, increase, multiply; also, to amount to, to increase co «xu to equal . whepsr, a; rhich; whichever. might, sb$ act; weight; signifying (a) the scales, (b) fcho thing uuighed, (a) the weight used us st;uidurd.

wlSte, «b; sea wight,

wise, sb; kind, typo,

wldocho, vj to sash.

vipye, eb; a withe -or strip of cano or weed,

wits, v; to kn-uv, have knowledge of. stlrt®, ■b| a sense, one of the five wonyngos, sb; (pi.) dwelling places, vTundo, sb; wind.

1 ydria, sb; (L) jug, water pot, urn. aerie, ebj twi^i stick, small rod, y3e , yhc, ob; eye. ylieb e, advj equally} likew ise. E^-n „ n m C5

39001 001284OT^b / f v / f9

E 9 7 9 1 94 1 192

DEDERICH R MttTREVlSAS TRANSLATION OF THE

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